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MATH225N Week 5 Assignment: Understanding Normal Distribution Q Rosetta averages 148 points per bowling game with a standard deviation of 14 points. Suppose Rosetta's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(148,14). If necessary, round to three decimal places. Ans: Suppose Rosetta scores 110 points in the game on Thursday. The z-score when x=110 is −2.714. The mean is $$148. This z-score tells you that x=110 is 2.714 standard deviations to the left of the mean. Q Suppose X∼N(12.5,1.5), and x=11. Find and interpret the z-score of the standardized normal random variable. Ans: The z-score when x=11 is −1. The mean is 12.5. This z-score tells you that x=11 is 1 standard deviation(s) to the left of the mean. Q Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
Ans: A has the larger mean. B has the larger mean. The means of A and B are equal. A has the larger standard deviation. B has the larger standard deviation. The standard deviations of A and B are equal. Q
Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. Ans: A has the larger mean. B has the larger mean. The means of A and B are equal. A has the larger standard deviation. B has the larger standasrd deviation. The standard deviations of A and B are equal. Q The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest mean.
Ans: A Q Hugo averages 22 points per basketball game with a standard deviation of 4 points. Suppose Hugo's points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(22,4). Ans: Suppose Hugo scores 7 points in the game on Sunday. The z-score when x=7 is 1. The mean is 2. This z-score tells you that x=7 is standard deviations to the left of the mean. Correct answers: Q Gail averages 64 words per minute on a typing test with a standard deviation of 9.5 words per minute. Suppose Gail's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(64,9.5). If necessary, round to three decimal places. Ans: Suppose Gail types 89 words per minute in a typing test on Sunday. The z-score when x = 89 is 1. The mean is 2.
Lexie averages 149 points per bowling game with a standard deviation of 14 points. Suppose Lexie's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(149,14). If necessary, round to three decimal places. Ans: Suppose Lexie scores 186 points in the game on Tuesday. The z-score when x = 186 is $$2.643. The mean is $$149. This z-score tells you that x = 186 is $$2.643 standard deviations to the right of the mean.
