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ID

Number

Name

Organizin

g

Guide

Evaluatin

g

proves

the

skills

MINITAB

King Abdul Aziz University

Faculty of Engineering

Electrical and Computer Engineering

Department

IE331 – Engineering Statistics and

Probability

Spring 2015

HOMEWORK 7

"BY USING MINITAB"

Instructors:

DR. Safa Elaskary

Eng. Wafa Abu alhasan

Submission date: May 17, 2015

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The Tasks:

ALL the following tasks are required to solve by MINITAB 17 only:

1. Search the internet to find any suitable set of data (at least 50 numbers). For this

set of data:

a. Calculate the mean, median , mode, 10% trimmed mean, range, variance and

standard deviation.

b. Construct a stem and leaf plot.

c. Construct a relative frequency histogram. Comment on the skewness.

d. Construct a box and whisker plot. Find the outliers (if any).

2. Resolve the following problems from Homework No. 4:

a. 5.1(a, d), Q5.3b, 5.5, 5.6.

b. 6.2a, 6.4(b, d), 6.7, 6.9a.

3. Resolve the following problems from Homework No. 5 & 6:

a. 8.4a, 8.5a, 8.6a.

b. 9.1a, 9.2.

c. 10.1, 10.2, 10.3.

4. Search the internet to find any suitable set of (x, y) data (at least 50 pairs). For this

set of data:

a. Draw a scatter diagram.

b. Estimate the linear regression line.

c. Compute and interpret the sample correlation coefficient.

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1. Search the internet to find any suitable set of data (at least 50 numbers).

37 25 21 22 10

33 26 32 35 30

22 15 18 20 21

30 42 24 40 21

15 18 16 22 33

22 36 32 40 44

20 42 45 28 24

21 44 22 33 41

45 43 38 35 33

19 22 44 38 27

For this set of data:

a. Calculate the mean, median , mode, 10% trimmed mean, range, variance and

standard deviation.

b. Construct a stem and leaf plot.

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c. Construct a relative frequency histogram. Comment on the skewness (NORMAL).

d. Construct a box and whisker plot. Find the outliers (if any).

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2. Resolve the following problems from Homework No. 4:

a. 5.1(a, d), Q5.3b, 5.5, 5.6.

Q5.1. In a certain city district, the need for money to buy drugs is stated as the reason for 70% of all thefts. Find the probability that among the next 6 theft cases reported in this district,: a. exactly 4 resulted from the need for money to buy drugs;

d. from 3 to 5 resulted from the need for money to buy drugs.

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Q5.3. From a lot of 15 missiles, 5 are selected at random and fired. If the lot contains 3 defective missiles that will not fire, what is the probability that: b. at most 2 will fire?.

Q5.5. Find the probability that a person flipping a fair coin gets: a. the third head on the seventh flip;

b. the first head on the fourth flip.

Q5.6. On average, a textbook author makes two word processing errors per page on the first draft of his textbook. What is the probability that on the next page he will make: a. 3 or more errors?

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b. no errors?

b. 6.2a, 6.4(b, d), 6.7, 6.9a.

Q6.2. Given a standard normal distribution, find the value of k such that: a. P(Z > k) = 0.3367;

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Q6.4. A soft-drink machine is regulated so that it discharges an average of 300 milliliters per cup. If the amount of drink is normally distributed with a standard deviation equal to 18 milliliters,: b. what is the probability that a cup contains between 290 and 322 milliliters?

d. below what value do we get the smallest 30% of the drinks?

Q6.7. Suppose that the time, in hours, required to repair a heat pump is a random variable X having a gamma distribution with parameters α = 3 and β = 1/2. What is the probability that on the next service call at least 2 hours will be required to repair the heat pump?

Cumulative Distribution Function Gamma with shape = 3 and scale = 0.5

x P( X <= x )

2 0.761897

so :

P( X >= 2 )= 1 - 0.761897 = 0.238103

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Q6.9. Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with a mean of 4 seconds. a. What is the probability that response time exceeds 6 seconds?

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3. Resolve the following problems from Homework No. 5 & 6:

a. 8.4a, 8.5a, 8.6a.

Q8.4. a. Find t0.025 when v = 12.

Q8.5. a. Find P(T < 2.365) when v = 7.

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Q8.6. Given a random sample of size 24 from a normal distribution, find k such that: a. P(−2.069 < T < k) = 0.965;

b. 9.1a, 9.2.

Q9.1. An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 42 hours. a. If a sample of 36 bulbs has an average life of 789 hours, find a 98% confidence interval for the population mean of all bulbs produced by this firm.

P (t> -2.069) = 0.975

P (t>k) = 0.01

K= 2.5

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Q9.2. A machine produces metal pieces that are cylindrical in shape. Assume their diameters follow approximately normal distribution. A sample of pieces is taken, and the diameters are found to be: 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 centimeters. a. Find a 99% confidence interval for the mean diameter of pieces from this machine.

b. Find a lower 99% confidence bound for the mean diameter of pieces from this machine if the population standard deviation is known and its value is 0.02 cm.

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c. 10.1, 10.2, 10.3.

Q10.1. A random sample of 64 bags of white popcorn weighed, on average, 152.3 grams with a standard deviation of 2.8 grams. Test the hypothesis that μ = 156 grams against the alternative hypothesis, μ < 156 grams, at the 0.05 level of significance.

Q10.2. Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are: 10.1, 9.8, 10.0, 10.5, 10.1, 9.6, 9.9, 10.4, 10.3, and 9.8 liters. Use a 0.03 level of significance and assume that the distribution of contents is normal.

Q10.3. It is claimed that automobiles are driven on average more than 20,000 kilometers per year. To test this claim, 110 randomly selected automobile owners are asked to keep a record of the kilometers they travel. Would you agree with this claim if the random sample showed an average of 23,200 kilometers and a standard deviation of 4,400 kilometers? Use a P-value in your conclusion.

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4. Search the internet to find any suitable set of (x, y) data (at least 50 pairs).

For this set of data:

a. Draw a scatter diagram.

(1,7) (2,2) (1,4) (0,2) (1,2)

(1,6) (5,1) (8,1) (7,2) (4,2)

(5,2) (1,9) (1,8) (4,4) (5,4)

(5,5) (9,7) (4,2) (7,4) (1,1)

(1,8) (7,6) (3,2) (4,2) (1,3)

(6,4) (5,6) (3,7) (5,9) (4,4)

(1,4) (7,8) (2,9) (1,7) (4,2)

(5,2) (4,5) (1,6) (7,2) (1,9)

(7,6) (9,6) (7,9) (8,7) (9,2)

(1,5) (9,2) (5,6) (8,9) (6,2)

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b. Estimate the linear regression line.

c. Compute and interpret the sample correlation coefficient.