MATH 225N WEEK 5 LAB ASSIGNMENT 2026 PRACTICAL LAB INTERPRETATION SET, Exams of Mathematical Modeling and Simulation

MATH 225N WEEK 5 LAB ASSIGNMENT 2026 PRACTICAL LAB INTERPRETATION SET

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2025/2026

Available from 02/02/2026

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MATH 225N WEEK 5 LAB ASSIGNMENT 2026
PRACTICAL LAB INTERPRETATION SET
◉ 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.) Answer: 0.241
◉ 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. Answer: 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. Answer: B
has the larger mean.
A has the larger standard deviation.
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MATH 225N WEEK 5 LAB ASSIGNMENT 2026

PRACTICAL LAB INTERPRETATION SET

◉ 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.) Answer: 0.2 41 ◉ 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. Answer: 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. Answer: B has the larger mean. A has the larger standard deviation.

◉ Which of the following tables shows a valid probability density function? Select all correct answers. Answer: 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 ◉ 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. Answer: 0. ◉ 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? Answer: 171 ◉ 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. Answer: 97.5% ◉ 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.

◉ 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. Answer: 16% (13.5+2.35+0.15=16) ◉ Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. Answer: The means of A and B are equal. (Peaks are aligned on x axis) A has the larger standard deviation. (more spread out) ◉