MATH 225N Week 5 Assignment; Understadning Normal Distribution..

MATH225N Week 5 Assignment: Understanding Normal Distribution Q1 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. Q2 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. Q3 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. 9144001746841118869392489 B has the larger mean. 9144001747661118869392571 The means of A and B are equal. 9144001747661118869392571 A has the larger standard deviation. 9144001747661118869392571 B has the larger standard deviation. 9144001747661118869392571 The standard deviations of A and B are equal. Q4 Ans: A has the larger mean. 9144001746841118869392489 B has the larger mean. 9144001747661118869392571 The means of A and B are equal. 9144001747661118869392571 A has the larger standard deviation. 9144001747661118869392571 B has the larger standard deviation. 9144001747661118869392571 The standard deviations of A and B are equal. Q5 Ans: A has the larger mean. 9144001746541118869392459 B has the larger mean. 9144001747661118869392571 The means of A and B are equal. 9144001747661118869392571 A has the larger standard deviation. 9144001747661118869392571 B has the larger standasrd deviation. 9144001747661118869392571 The standard deviations of A and B are equal. Q6 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 Q7 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). 5838190147800Ans: 1054100389098Suppose Hugo scores 7 points in the game on Sunday. The z-score when x=7 is 1. The mean is 2. 2948939-54493 3 This z-score tells you that x=7 isstandard deviations to the left of the mean. Correct answers: 1$-3.75$−3.75 2$22$22 3