# (Answered) MATH399N Week 5 Quiz

question 1

Peter has collected data to find that the finishing times for cyclists in a race has a normal distribution. Based on the Empirical Rule, what is the probability that a randomly selected race participant had a finishing time of greater than 171 minutes if the mean is 156 minutes and the standard deviation is 15 minutes? Enter your answer as a percent rounded to 2 decimal places if necessary. Include the percent symbol % in your answer.

QUESTION 2

A softball pitcher has a 0.626 probability of throwing a strike for each curve ball pitch. If the softball pitcher throws 30 curve balls, what is the probability that no more than 16 of them are strikes?

## QUESTION 3

A casino features a game in which a weighted coin is tossed several times. The table shows the probability of each payout amount. To the nearest dollar, what is expected payout of the game?

### QUESTION 4

Alice was told that her reading test score was 1 standard deviation below the mean. If test scores were approximately normal with μ=86 and σ=4, what was Alice’s score? Do not include units in your answer. For example, if you found that the score was 86 points, you would enter 86.

QUESTION 5

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

QUESTION 6

Which of the following tables shows a valid probability density function? Select all correct answers.

QUESTION 7

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

QUESTION 8

Find the area to the right of the z-score 1.40 and to the left of the z-score 1.58 under the standard normal curve.

# QUESTION 9

Gail averages 153 points per bowling game with a standard deviation of 14.5 points. Suppose Gail’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(153,14.5).

If necessary, round to three decimal places.

### QUESTION 10

The total snowfall per year in Laytonville is normally distributed with mean 99 inches and standard deviation 14 inches. Based on the Empirical Rule, what is the probability that in a randomly selected year, the snowfall was less than 127 inches? Enter your answer as a percent rounded to 2 decimal places if necessary.

QUESTION 11

A fair coin is flipped 104 times. Let X be the number of heads. What normal distribution best approximates X?

• Round to one decimal place if entering a decimal answer below.

QUESTION 12

A random sample of math majors taking an introductory statistics course were surveyed after completing the final exam. They were asked, “How many times did you review your final exam before handing it in to the professor?” The results are displayed in a probability density function for the random variable X, the number of times students reviewed their exam before handing it in. Find the standard deviation of X.

• Round the final answer to two decimal places.

### QUESTION 13

On average, Nancy has noticed that 22 trucks pass by her apartment daily (24 hours). In order to find the probability that more than 5 trucks will pass her apartment in a 6-hour time period using the Poisson distribution, find the average number of trucks per 6 hours. Round your answer to three decimal places, if necessary.

### QUESTION 14

On average, Ashton has noticed that 17 trains pass by his house daily (24 hours) on the nearby train tracks. What is the probability that at most 6 trains will pass his house in a 7-hour time period? (Round your answer to three decimal places.)

### QUESTION 15

Identify the parameter p in the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 0.702, and the probability of buying a movie ticket without a popcorn coupon is 0.298. If you buy 23 movie tickets, we want to know the probability that more than 15 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)

# Solution:

question 1

Peter has collected data to find that the finishing times for cyclists in a race has a normal distribution. Based on the Empirical Rule, what is the probability that a randomly selected race participant had a finishing time of greater than 171 minutes if the mean is 156 minutes and the standard deviation is 15 minutes? Enter your answer as a percent rounded to 2 decimal places if necessary. Include the percent symbol % in your answer.