UNIVERSITY OF TORONTO SCARBOROUGH …mahinda/stab22/b22mt16s_e.pdfPage 2 of 22 1.In order to study...

UNIVERSITY OF TORONTO SCARBOROUGHDepartment of Computer and Mathematical Sciences

Midterm Test June 2016

STAB22H3 Statistics IDuration: 1 hour and 45 minutes

Last Name: First Name:

Student number:

Aids allowed:

- One handwritten letter-sized sheet (both sides) of notes prepared by you

- Non-programmable, non-communicating calculator

Standard normal distribution tables are attached at the end.

This test is based on multiple-choice questions. The are 35 questions. All questions carryequal weight. On the Scantron answer sheet, ensure that you enter your last name, firstname (as much of it as fits), and student number (in “Identification”).

Mark in each case the best answer out of the alternatives given (which means the nu-merically closest answer if the answer is a number and the answer you obtainedis not given.)

Also before you begin, complete the signature sheet, but sign it only when the invigilatorcollects it. The signature sheet shows that you were present at the exam.

There are 22 pages including this page. Please check to see you have all the pages.

Good luck!!

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1. In order to study the popular choices of bicycles among university students, a bicyclemanufacturer conducted a survey of bicycles parked outside student residences at auniversity. The survey recorded the style (mountain bike, road bikes, etc.), the brand,the color, and the age. Identify the W’s for this data. (Note: In this question you onlyhave to identify three W’s, who, what and why).

A) Who: Student residences; What: Type of student residence; Why: To studythe popular choices of bicycles among university students

B) Who: Bicycles parked outside student residences; What: Style, brand, color,and age of bicycle; Why: To study the popular choices of bicycles amonguniversity students

C) Who: Bicycles parked on campus; What: Style, brand, color, and age ofbicycle; Why: Class Assignment

D) Who: Bicycles parked outside student residences; What: Mountain bikes;Why: To study the popular choices of bicycles among university students

E) Who: Student residences; What: Size of student residence; Why: Not specified

2. When a set of data has outliers, which of the following are preferred measures of centreand spread?

A) Mean and standard deviation

B) Median and Range

C) Mean and range

D) Median and interquartile range

E) Median and standard deviation

3. In a demographic survey, a researcher collected data on the following variables. Whichof them is an ordinal variable?

A) Annual income in dollars

B) Ethnicity (White, Hispanic, African American etc)

C) Education (below high school, high school diploma, University degree)

D) Marital Status (single, married, widowed, divorced, separated)

E) Employment status (employed for wages,self-employed, looking for work, re-tired)

4. In a study of the distribution of colour of baby voles (A vole is a small rodent), a re-searcher recorded the colour of 20 baby voles shown below (B = brown, G = gray, W =white, and T = tan):

B, W, B, G, B, B, G, B, G, B, B, B, T, G, T, B, B, B, W, G

Which of the following bar charts represent the bar chart for this data set.

Question 4 continues on the next page. . .

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B G T W

Bar Chart A

Colour

Fre

quen

cy

02

46

810

B G T W

Bar Chart B

ColourF

requ

ency

02

46

810

B G T W

Bar Chart C

Colour

Fre

quen

cy

01

23

45

67

B G T W

Bar Chart D

Colour

Fre

quen

cy

01

23

45

6

B G T W

Bar Chart E

Colour

Fre

quen

cy

01

23

45

67

A) Bar chart A

B) Bar chart B

C) Bar chart C

D) Bar chart D

E) Bar chart E

5. In a study, a group of children were asked what their favourite flavour of ice cream is.The pie chart below shows their responses. If 15 children in this group said mint istheir favourite flavour, then how many children in the group said vanilla is their fvouriteflavour?


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vanilla 30%

chocolate 32%

mint 10%strawberry 28%

Pie Chart of favourite flavour of ice cream

A) 5 children

B) 15 children

C) 30 children

D) 45 children

E) 60 children

6. If a histogram of a quantitative variable is multi-modal (i.e has more than one mode),which of the following must be true.

A) The histogram must be symmetric.

B) The histogram must be skewed to the left.

C) The histogram must be skewed to the right.

D) The mean and the median must be equal.

E) None of the above is true.

7. The histogram below displays the distribution of the systolic blood pressure (mm Hg) ofa group of patients. What percentage of the patients in this group had a systolic bloodpressure reading greater than 140.Note: In order to avoid unnecessary complications, you may assume that there were nopatients with systolic blood pressure exactly at any of the class boundaries.


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Systolic Blood Pressure

Frequency

24020016012080

40

30

20

10

0

Histogram of Systolic Blood Pressure

A) 43.5 percent

B) 50 percent

C) 56.5 percent

D) 65 percent

E) 77 percent

Solution: (30 + 10 + 5 + 5)/(5 + 20 + 40 + 30 + 10 + 5 + 5) = 0.4347826087 = 43.5 %

8. Which of the following statements is/are true of the data shown in the histogram below?


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x

Frequency

70605040302010

7

6

5

4

3

2

1

0

Histogram of x

I The distribution is skewed to the right.

II The mean of this data set is smaller than the median.

III We should use the mean and the standard deviation to summarize these data.

A) Only I is true.

B) Only II is true.

C) Only III is true.

D) Only I and II are true.

E) Only II and III are true.

Solution: This distribution is left skewed. For left skewed distributions, means issmaller than the median. For skewed distributions mean and standard deviation arenot appropriate. Use median and IQR.

9. The stemplot below shows the distribution of the survival times in days of 22 guineapigs after they were injected with infectious bacteria in a medical experiment. What isthe inter-quartile range(IQR) of the survival times of these guinea pigs?

The decimal point is 1 digit(s) to the right of the colon.


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4 : 35

5 : 36678

6 : 67

7 : 349

8 : 0011123589

A) 2.4 days

B) 24 days

C) 46 days

D) 57 days

E) 81 days

Solution: Q1 = 57, Q3 = 81 and IQR = Q3−Q1 = 81− 57 = 24

R output is shown below:

> x <- c(43, 45, 53, 56, 56, 57, 58, 66, 67, 73, 74, 79 ,80,

80, 81, 81, 81 ,82 ,83, 85, 88, 89)

> stem(x)

The decimal point is 1 digit(s) to the right of the |

4 | 35

5 | 36678

6 | 67

7 | 349

8 | 0011123589

> length(x)

[1] 22

> summary(x)

Min. 1st Qu. Median Mean 3rd Qu. Max.

43.00 57.25 76.50 70.77 81.00 89.00

> IQR(x)

[1] 23.75

>

10. The boxplot of the cholesterol levels of a group of 60 people is shown below. (You mayassume that this is a data set with 60 distinct values, i.e. no two people in this grouphave the same cholesterol level.)


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Based on this information, which of the following statements is true?

A) 30 people in this group had cholesterol level between 180 and 210 mg perdecilitre.

B) 25 percent of the people in this group had cholesterol level below 210 mg perdecilitre.

C) 50 percent of the people in this group had cholesterol level between 190 and210 mg per decilitre.

D) 75 percent of the people in this group had cholesterol levels less than 180 mgper decilitre.

E) None of the above statements is true.

11. Refer to information in question 10 above. Which of the following summary measuresare the most appropriate statistics for summarizing the cholesterol data?

A) Mean and standard deviation

B) Mean and inter-quartile range

C) Median and inter-quartile range

D) Median and standard deviation

E) Mean and median

12. If a histogram of a quantitative variable has two modes, which of the following must betrue?

A) The histogram must be symmetric.


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B) The histogram must be bell-shaped

C) The histogram must be skewed to the left.

D) The histogram must be skewed to the right.

E) None of the above statements is true.

13. The boxplot of quiz grades in Statistics class is shown below. The grades were given outof 20.

Based on this information, which of the following statements is/are true?

I The distribution of these quiz grades is right skewed.

II The class median is less than 14.

III The Inter-quartile range is 8.

A) Only statement I is true.

B) Only statement II is true.

C) Only statement III is true.

D) Only statements I and III are true.

E) Only statements II and III are true.

14. Which of the following graphs is appropriate for displaying the distribution of a singlenominal categorical variable?

A) Histogram


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B) Stemplot

C) Boxplot

D) Scatterplot

E) None of the above

15. Which of the following data values (if any) would be considered an outlier according tothe 1.5(IQR) rule for identifying outliers?

5, 9, 13, 15, 22, 22, 23, 30, 36, 55

The Five-number summary is: 5, 13, 22, 30, 55Note: If you need any value in the five number summary to answer this question, usethe values in the five number summary provided above. Do NOT calculate them again.

A) 36 and 55 only

B) 55 only

C) 5 and 55 only

D) 5 only

E) There are no outliers.

Solution: LF = Q3− 1.5× IQR = 13− 1.5× (30− 13) = −12.5, UF = Q3 + 1.5×IQR = 30 + 1.5× (30− 13) = 55.5. No values outside the fences and so no outliers.

16. Which of the following is NOT a measure of spread?

A) Standard deviation

B) Median

C) Variance

D) Range

E) Inter-quartile range

17. If the variance of a distribution is 9, the standard deviation is:

A) 3

B) 6

C) 9

D) 81

E) −3

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18. Suppose a dentist office keeps track of the number of new cavities discovered during achilds dental exam. The mean number of new cavities is 1.15 with a standard deviationof 0.35. The childs parents are charged $50 for the exam plus $20 for the treatment ofeach cavity. The total cost (exam plus treatment) for a child with X cavities is 50+20X.What is the mean and standard deviation of the total cost, 50 + 20X?

A) mean = 73 and standard deviation = 57

B) mean = 73 and standard deviation = 7

C) mean = 77.5 and standard deviation = 57

D) mean = 77.5 and standard deviation = 7

E) mean = 51.15 and standard deviation = 50.35

Solution: mean = 50 + 20× 1.15 = 73, standard deviation = 20× 0.35 = 7 and sothe answer is B.

19. The length (in centimeters) of a randomly selected fish from a particular lake has aNormal distribution with mean 15 cm and standard deviation 5 cm. What percentageof these fish are longer than 18 cm?

A) 60 percent

B) 72.6 percent

C) 27.4 percent

D) 30 percent

E) 25 percent

Solution: z = (18−15)/5 = 0.60, and the table value is 0.7257 and so the proportionlonger than 18 cm is 1 - 0.7257 = 0.2743. The percentage is 27.43.

20. The heights of the students in a school are Normally distributed with mean 68 inches andstandard deviation 2 inches. Only about 5% of all students in this school have heightsoutside the range

A) 66 inches to 70 inches.

B) 64 inches to 72 inches.

C) 62 inches to 74 inches.

D) 58 inches to 78 inches.

E) 60 inches to 76 inches.

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Solution: Using 68-95-99.7 rule: (68− 2× 2, 68 + 2× 2) = (64, 72)Using Normal tables: (68 − 1.96 × 2, 68 + 1.96 × 2) = (64.08, 71.92) = (64, 72) thesame as 68-95-99.7 rule.

21. The average time students need to finish a particular test is 70 minutes with a standarddeviation of 12 minutes. Assume that these times are Normally distributed. The in-structor wants 90% of the students to have sufficient time to finish the test. How muchtime should be allowed in order to ensure that 90% of the students will finish the testduring the time allowed?

A) 55 minutes

B) 82 minutes

C) 85 minutes

D) 90 minutes

E) 94 minutes

Solution: z value for 0.90 is 1.28 and so the required time is 70 + 12× 1.28 = 85.36

The R output is shown below:

> qnorm(0.90, 70, 12)

[1] 85.37862

22. Which of the following statements about the Normal distribution or the Normal densitycurves is NOT true?

A) The area below any Normal density curve (and above the horizontal axis) isequal to 1.0.

B) Every Normal distribution has its mean equal to its median.

C) Every Normal density curve is symmetric about its mean.

D) Every Normal density curve is bell-shaped.

E) Every Normal distribution has standard deviation equal to 1.

23. The following statistics were produced at the end of a week, at a weight loss centre indi-cating pounds lost of their weight watchers who participated in a weight loss program:

mean = 5 lbsfirst quartile = 2.0 lbsmedian = 7 lbsthird quartile = 8.5 lbsstandard deviation = 0.5 lbsBased on this information, which of the following statements is/are true?


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I One quarter of weight watchers lost 2 lbs or less.

II Middle 50% of the weight watchers lost between 2 and 8.5 lbs.

III The distribution of the pounds lost is skewed to the right.

A) I only

B) II only

C) III only

D) I and II only

E) I, II and III

24. John takes the bus to work everyday. His waiting time for the bus varieties from 5 to25 minutes according to the density shown below. What proportion of days he waitsbetween 10 to 18 minutes for the bus?

Density

Waiting time5 25

A) 0.2

B) 0.4

C) 0.6

D) 0.8

E) 0.5

Solution: (18− 10)/(25− 5) = 8/20 = 0.4

25. The graph below shows that density curve of a variable. One point on the horizontalaxis of the graph below is indicated by T . What is the value of T

Density

x

0.25

T


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A) 1

B) 2

C) 3

D) 4

E) 5

Solution: T = 1/0.25 = 4

26. A study found a correlation of r = −0.575 between hours spent watching television andhours per week spent exercising. Which of the following statements is true?

A) Approximately 33 percent of the variation in hours spent exercising can beexplained by liner regression with hours spent watching television.

B) A person who watches less television will exercise more.

C) For each hour spent watching television, the predicted decrease in hours spentexercising is 0.575 hours.

D) There is a cause-and-effect relationship between hours spent watching televi-sion and a decline in hours spent exercising.

E) 57.5 percent of the variation in hours spent exercising can be explained byliner regression with hours spent watching television.

Solution:√

0.575 = 0.331 =≈ 33 %.

27. Environmental researchers have collected data on rain acidity for years. Suppose that aNormal distribution describes the acidity (pH value) of rainwater, and that water testedafter a particular storm had a z-score of 1.8. This means that the acidity of that rainafter that particular storm . . .

A) had pH value 1.8.

B) had a pH value 1.8 times the mean pH value.

C) had a pH value 1.8 standard deviations higher than the mean pH value.

D) had a pH value 1.8 higher than average rainfall.

E) had a pH value 1.8 lower than average rainfall.

28. Three statistics classes (50 students each) took the same test. Shown below are his-tograms of the scores for the classes. Use the histograms to answer the question.


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For which class are the mean and median most different? Give reasons for your answer.

A) Class 2, because the shape is symmetric.

B) Class 1, because the shape is skewed to the left.

C) Class 3, because the shape is symmetric.

D) Class 1, because the shape is symmetric.

E) Class 2, because the shape is skewed to the left.

29. Shown below are the histogram and summary statistics for the weekly salaries (in dollars)of 24 randomly selected employees of a company:

Choose the boxplot that represents the given data.


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A) Boxplot I

B) Boxplot II

C) Boxplot III

D) Boxplot IV

E) Boxplot V

30. A survey of automobiles parked in student and staff lots at a large university classifiedthe brands by country of origin, as seen in the table.

DriverOrigin Student StaffNorth American 91 90European 31 16Asian 68 54

What is the marginal distribution of origin?

A) 52% North American, 13% European, 35% Asian

B) 56% North American, 10% European, 34% Asian

C) 54% Students, 46% Staff

D) 107% North American, 16% European, 54% Asian

E) 48% North American, 16% European, 36% Asian

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Solution: North American (91+90)/(91+90+31+16+68+54) = 0.52, European: (91+91)/(91+90+31+16+68+54)= 13, Asian = (68+54)/(91+90+31+16+68+54) = 0.35.

31. A public opinion survey explored the relationship between age and support for increasingthe minimum wage. The results are summarized in table the below.

Age group Support Against No opinion21-40 25 20 541-60 20 35 20Over 60 55 15 5

What is the conditional percentage of supporters of increasing the minimum wage, amongthose who are in age group 21-40?

A) 12.5 %

B) 20 %

C) 25 %

D) 50 %

E) 75%

Solution: A total of 50 people in the 21 to 40 age group were surveyed. Of those,25 were for increasing the minimum wage. Thus, half of the respondents in the 21to 40 age group (50%) supported increasing the minimum wage.

32. A scatterplot of a response variable y against an explanatory variable x is given below.


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Which of the following options best describes the relationship between the two variables?

A) Positive association, linear association, weak association

B) non-linear association, moderately strong association

C) Positive association, linear association, strong association

D) Negative association, linear association, moderately strong association

E) Negative association, linear association, weak association

33. A random sample of records of electricity usage of homes in the month of July gives theamount of electricity used and size (in square feet) of 135 homes. A regression was doneto predict the amount of electricity used (in kilowatt-hours) from size (square feet). Theresiduals plot indicated that a linear model is appropriate. The slope of the regressionline is 0.5 and the y-intercept is 1240. What is the predicted electricity usage in a housethat is 2,372 square feet?

A) 54 kilowatt-hours

B) 2,264.00 kilowatt-hours

C) 1,186 kilowatt-hours

D) 2,426 kilowatt-hours

E) 1,806 kilowatt-hours

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Solution: 1240 + 0.5× 2372 = 2426

34. A golf ball is dropped from 15 different heights (in cm) and the height of the bounce is

recorded (in cm.) The regression analysis gives the model bounce = 0.3 + 0.74 × drop.A golf ball dropped from a height 61 cm, bounced 46.44 cm. What is the residual forthis bounce height?

A) -1 cm

B) 0.74 cm

C) 46.14 cm

D) 1 cm

E) 2 cm

Solution: Residual = y − y = 46.44− (0.3 + 0.74× 61) = 1

35. The Normal quantile plot for a data set is shown below.

Based on this plot, what can we say about the distribution of this data?

A) The distribution is Normal because the Normal quantile plot is non-linear.


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B) The distribution is symmetric because the Normal quantile plot is non-linear.

C) The distribution is skewed to the left.

D) The distribution is skewed to the right.

E) The distribution is uniform because the Normal quantile plot is linear.

END OF TEST

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Tables of normal, binomial and t-distributionsprepared by Ken Butler

2015-06-03

Table Z (normal distribution)

Values of z greater than 0 are on the next page. Second decimal place is at the top of the column.0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00

-3.8 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001-3.7 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001-3.6 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002-3.5 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002-3.4 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003-3.3 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005-3.2 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007 0.0007-3.1 0.0007 0.0007 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009 0.0010-3.0 0.0010 0.0010 0.0011 0.0011 0.0011 0.0012 0.0012 0.0013 0.0013 0.0013-2.9 0.0014 0.0014 0.0015 0.0015 0.0016 0.0016 0.0017 0.0018 0.0018 0.0019-2.8 0.0019 0.0020 0.0021 0.0021 0.0022 0.0023 0.0023 0.0024 0.0025 0.0026-2.7 0.0026 0.0027 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035-2.6 0.0036 0.0037 0.0038 0.0039 0.0040 0.0041 0.0043 0.0044 0.0045 0.0047-2.5 0.0048 0.0049 0.0051 0.0052 0.0054 0.0055 0.0057 0.0059 0.0060 0.0062-2.4 0.0064 0.0066 0.0068 0.0069 0.0071 0.0073 0.0075 0.0078 0.0080 0.0082-2.3 0.0084 0.0087 0.0089 0.0091 0.0094 0.0096 0.0099 0.0102 0.0104 0.0107-2.2 0.0110 0.0113 0.0116 0.0119 0.0122 0.0125 0.0129 0.0132 0.0136 0.0139-2.1 0.0143 0.0146 0.0150 0.0154 0.0158 0.0162 0.0166 0.0170 0.0174 0.0179-2.0 0.0183 0.0188 0.0192 0.0197 0.0202 0.0207 0.0212 0.0217 0.0222 0.0228-1.9 0.0233 0.0239 0.0244 0.0250 0.0256 0.0262 0.0268 0.0274 0.0281 0.0287-1.8 0.0294 0.0301 0.0307 0.0314 0.0322 0.0329 0.0336 0.0344 0.0351 0.0359-1.7 0.0367 0.0375 0.0384 0.0392 0.0401 0.0409 0.0418 0.0427 0.0436 0.0446-1.6 0.0455 0.0465 0.0475 0.0485 0.0495 0.0505 0.0516 0.0526 0.0537 0.0548-1.5 0.0559 0.0571 0.0582 0.0594 0.0606 0.0618 0.0630 0.0643 0.0655 0.0668-1.4 0.0681 0.0694 0.0708 0.0721 0.0735 0.0749 0.0764 0.0778 0.0793 0.0808-1.3 0.0823 0.0838 0.0853 0.0869 0.0885 0.0901 0.0918 0.0934 0.0951 0.0968-1.2 0.0985 0.1003 0.1020 0.1038 0.1056 0.1075 0.1093 0.1112 0.1131 0.1151-1.1 0.1170 0.1190 0.1210 0.1230 0.1251 0.1271 0.1292 0.1314 0.1335 0.1357-1.0 0.1379 0.1401 0.1423 0.1446 0.1469 0.1492 0.1515 0.1539 0.1562 0.1587-0.9 0.1611 0.1635 0.1660 0.1685 0.1711 0.1736 0.1762 0.1788 0.1814 0.1841-0.8 0.1867 0.1894 0.1922 0.1949 0.1977 0.2005 0.2033 0.2061 0.2090 0.2119-0.7 0.2148 0.2177 0.2206 0.2236 0.2266 0.2296 0.2327 0.2358 0.2389 0.2420-0.6 0.2451 0.2483 0.2514 0.2546 0.2578 0.2611 0.2643 0.2676 0.2709 0.2743-0.5 0.2776 0.2810 0.2843 0.2877 0.2912 0.2946 0.2981 0.3015 0.3050 0.3085-0.4 0.3121 0.3156 0.3192 0.3228 0.3264 0.3300 0.3336 0.3372 0.3409 0.3446-0.3 0.3483 0.3520 0.3557 0.3594 0.3632 0.3669 0.3707 0.3745 0.3783 0.3821-0.2 0.3859 0.3897 0.3936 0.3974 0.4013 0.4052 0.4090 0.4129 0.4168 0.4207-0.1 0.4247 0.4286 0.4325 0.4364 0.4404 0.4443 0.4483 0.4522 0.4562 0.46020.0 0.4641 0.4681 0.4721 0.4761 0.4801 0.4840 0.4880 0.4920 0.4960 0.5000

1

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Table Z (continued)

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.53590.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.57530.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.61410.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.65170.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.68790.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.72240.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.75490.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.78520.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.81330.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.83891.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.86211.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.88301.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.90151.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.91771.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.93191.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.94411.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.95451.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.96331.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.97061.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.97672.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.98172.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.98572.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.98902.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.99162.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.99362.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.99522.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.99642.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.99742.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.99812.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.99863.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.99903.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.99933.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.99953.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.99973.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.99983.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.99983.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.99993.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.99993.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

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