APS- Unit 4: Randomness & Probability

The Safe Drinking Water Hotline routinely tracks requests for information about water quality. The table above shows the sources of some of its calls.

What is the probability that a request comes from a school given that it is an e-mail request?

• 1/62

• 1/63

• 1/82

• 1/117

• 64/90,123

At Kennett High School, 5% of athletes play both football and some other contact sport, 30% play football, and 40% play other contact sports. If there are 200 athletes, how many play neither football nor any other contact sport?

• 20

• 70

• 80

• 200

• 130

The Correcto Publishing Company claims that its publications will have errors only twice in every 100 pages. What is the approximate probability that Anne will read 235 pages of a 790-page book published by Correcto before finding an error?

• 0.02%

• 2%

• 5%

• 16%

• 30%

The theoretical probability of rolling a 2 or a 6 one one roll of a die is ⅓. A student who tries to reproduce this probability by counting successes in repeated trials is most likely to come closest to ⅓ with:

• one roll of the die.

• two rolls of the die.

• three rolls of the die.

• ten rolls of the die.

• 100 rolls of the die.

For the sake of efficiency, a show company decides to produce the left shoe of each pair at one site and the right shoe at a different site. If the two sites produce shoes with a number of defects reflected by

μ₁ = 0.002, σ₁ = 0.15 and μ₂ = 0.005, σ₂ = 0.18.

What is the mean and standard deviation for the number of defects for pairs of shoes produced by this company?

• μ = 0.00035, σ = 0.165

• μ = 0.00035, σ = 0.0549

• μ = 0.007, σ = 0.0549

• μ = 0.007, σ = 0.2343

• μ = 0.007, σ = 0.33

The probability of a certain genetic trait in the general population is 27%. What is the expected number of people you would need to observe before finding one person with this trait?

• about 4

• about 10

• about 27

• about 73

• Not enough information is given to answer the question.

A recent survey of students at John Tukey High School revealed that 18% of the students are in favor of changing the dress code. If you randomly select 15 students from this school, what is the probability that at least three of these students are in favor of the proposal to change the dress code?

• 0.18³

• (0.18)³(0.82)¹²

• ₁₅C₃ (0.18)³(0.82)¹²

• 
• 

On a recent test in an introductory economics course, the mean grade was 42 with a variance of 9. Suppose that the distribution of students' scores on this test is given by the random variable X. The professor decides to curve the test by multiplying each score by 1.5 and then adding 7 more points to the result. The new mean and standard deviation for the scores are:

• 63, 4.5

• 63, 7.5

• 70, 4.5

• 70, 7.5

• 70, 20.25

Given two events A and B, if the probability that A occurs is 0.3, the probability that B occurs is 0.4, and the probability that A or B occurs is 0.55, then the P(A I B) is:

• 0.120

• 0.220

• 0.375

• 0.500

• 0.700

A game of chance involves rolling a fair die. If the die shows a 1, you win $4; if it shows a 2, you win $0.50; and if it shows any other number, you win nothing. If the cost to play the game is $1, what are a player's expected winnings?

• Lose $0.08

• Lose $0.25

• Win $0.08

• Win $0.25

• Win $0.75