Prob Stat review solutions -...
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Unit 6 Probability & Statistics Review 1. There are 12 people on a basketball team, and the coach needs to choose 5 to put into a game. How many different possible ways can the coach choose a team of 5 if each person has an equal chance of being selected? 1) 2) 3) 4) All players have an equal chnce means order doesn’t matter permutations (larger number always comes first) 2. A basketball squad has ten players. Which expression represents the number of five-player teams that can be made if John, the team captain, must be on every team? 1) 2) 3) 4) John’s in, so only 9 players left to choose the other 4 starters from, Again order doesn’t matter permutations 3. If the Math Olympiad Club consists of eighteen students, how many different teams of four students can be formed for competitions? 1) 66 2) 72 3) 3,060 4) 73,440 Permutations = !" ! 4. Which expression represents the number of different 8-letter arrangements that can be made from the letters of the word "SAVANNAH" if each letter is used only once? 1) 2) 3) 4) 8 letters, 3 As repeated, 2 Ns repeated 5. Dave is the manager of a construction supply warehouse and notes that 60% of the items purchased are heating items, 25% are electrical items, and 15% are plumbing items. Find the probability that at least three out of the next five items purchased are heating items. means 3 or 4 or 5 , and or tells you to add exactly 3 of 5 = ! ! 6 10 ! 4 10 ! = 216 625 plus exactly 4 of 5 = ! ! 6 10 ! 4 10 ! = 164 625 plus exactly 5 of 5 = ! ! 6 10 ! 4 10 ! = 243 3125 equals !"#$ !"#$
Transcript of Prob Stat review solutions -...
Unit 6 -‐ Probability & Statistics Review
1. There are 12 people on a basketball team, and the coach needs to choose 5 to put into a game. How many different possible ways can the coach choose a team of 5 if each person has an equal chance of being selected? 1) 2) 3) 4) All players have an equal chnce means order doesn’t matter à permutations (larger number always comes first) 2. A basketball squad has ten players. Which expression represents the number of five-player teams that can be made if John, the team captain, must be on every team? 1) 2) 3) 4) John’s in, so only 9 players left to choose the other 4 starters from, Again order doesn’t matter à permutations 3. If the Math Olympiad Club consists of eighteen students, how many different teams of four students can be formed for competitions? 1) 66 2) 72 3) 3,060 4) 73,440 Permutations = !"𝑃!
4. Which expression represents the number of different 8-letter arrangements that can be made from the letters of the word "SAVANNAH" if each letter is used only once? 1)
2)
3) 4) 33
8 letters, 3 As repeated, 2 Ns repeated 5. Dave is the manager of a construction supply warehouse and notes that 60% of the items purchased are heating items, 25% are electrical items, and 15% are plumbing items. Find the probability that at least three out of the next five items purchased are heating items.
means 3 or 4 or 5 , and or tells you to add
𝑃 exactly 3 of 5 = !𝐶! 610
! 410
!
= 216625
plus
𝑃 exactly 4 of 5 = !𝐶! 610
! 410
!
= 164625
plus
𝑃 exactly 5 of 5 = !𝐶! 610
! 410
!
= 2433125
equals !"#$
!"#$
Unit 6 -‐ Probability & Statistics Review
6. Beth’s scores on the six Earth science tests she took this semester are:
100, 95, 55, 85, 75, 100 For this population, how many scores are within one standard deviation of the mean? Find mean, standard deviation on calc –
1) STAT à EDIT to enter data
2) STAT à CALC à I-VAR STATS, Enter
𝑥 = 85, 𝜎! = 16.1 Mean + 1 Standard deviation à 85 + 16.1 = 101.1 Mean - 1 Standard deviation à 85 - 16.1 = 68.9 How many scores between 68.9 and 101.1? 5 7. The scores of one class on the Unit 2 mathematics test are shown in the table below.
Find the population standard deviation of these scores, to the nearest tenth.
Find standard deviation on calc –
1) STAT à EDIT to enter data in L1, frequency in L2
2) STAT à CALC à 1-VAR STATS List : L1 FreqList: L2
𝑥 = 79.4545… 𝑥 = 1748 𝑥! = 140080 𝑆𝑥 = 7.5385…
𝜎𝑥 = 7.3653… 𝑛 = 22 std. dev. – 𝜎𝑥 = 7.4 8. On a standardized test with a normal distribution, the mean was 64.3 and the standard deviation was 5.4. What is the best approximation of the percent of scores that fell between 61.6 and 75.1? 1) 38.2% 2) 66.8% 3) 68.2% 4) 95% 61.6 = 𝑥 − 0.5×5.4 mean -‐ one-‐half std. dev. 75.1 = 𝑥 + 2×5.4 mean + 2 std. dev. Add %s from -.5 to +2 9. In a certain population, the mean score on a test is 420. The standard deviation is 105. If the distribution of scores is normal, which of these scores should occur most often? 1) 540 2) 526 3) 385 4) 314
Score closest to the mean will show up the most
10. Which graph represents data used in a linear regression that produces a correlation coefficient closest to ? 1)
2)
3)
Unit 6 -‐ Probability & Statistics Review
4)
Correlation coefficient (r) tells how well the line fits. Positive 1 is perfect, as is negative 1. Only difference is slope (going up, or down). Zero is the worst.
11. The scores on a 100 point exam are normally distributed with a mean of 80 and a standard deviation of 6. A student's score places him between the 69th and 70th percentile. Which of the following best represents his score? 1) 66 2) 81 3) 84 4) 86 Complete the normal curve – mean (80) at the top, 86 at +1, 92 at +2, etc. Percentiles – add percents from left to right, until you get to 69% – at +0.5 std. dev., about 84 12. The fifth term in the expansion of is 6th power à 7 terms ___ ___ ___ ___ ___ ___ ___ Exponents - (2x) starts at 6 & counts down; (-y) starts at 0 and counts up. coefficient – from Pascal’s Triangle or formula 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1
15 ∙ 2𝑥 ! −𝑦 ! = 60𝑥!𝑦!
5th term
