Week 5 Quiz- MTH 399

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.

16% (13.5+2.35+0.15=16)

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?

171

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.

0.0237

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? Round your answer to 3 decimal places.

0.194

On average, Sean has noticed that 18 trains pass by his house daily (24 hours) on the nearby train tracks. What is the probability that at most 5 trains will pass his house in a 10-hour time period? (Round your answer to three decimal places.)

0.241

On average, Nancy has noticed that 17 trucks pass by her apartment daily (24 hours). In order to find the probability that more than 4 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.

0.420

Identify the parameter p in the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 0.754, and the probability of buying a movie ticket without a popcorn coupon is 0.246. If you buy 17 movie tickets, we want to know the probability that more than 11 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)

0.754

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.

2.64

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.

52, 5.1

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.

82

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.

97.5%

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

B has the larger mean. A has the larger standard deviation.

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.

Suppose Gail scores 108 points in the game on Thursday. The z-score when x = 108 is −3.103. The mean is 153. This z-score tells you that x = 108 is 3.103 standard deviations to the left of the mean.

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

The means of A and B are equal. (Peaks are aligned on x axis) A has the larger standard deviation. (more spread out)

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

the values of P(X=x) must add up to 1 if there is a negative value of P(X=x) then it is invalid