Mathematics > EXAM > math 225n week-5-understanding-normal-distribution-complete-solutions-guide (All)

math 225n week-5-understanding-normal-distribution-complete-solutions-guide

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• 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. T... hen X∼N(149,14). Suppose Lexie scores 186 points in the game on Tuesday. The z-score 2.643 when x = 186 is - no response given. The mean is - no 149 response given. This z-score tells you that x = 186 is 2.643- no response given standard deviations to the right of the mean. The z-score can be found using this formula: z=x−μσ=186−149/14=3714≈2.643 The z-score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. So, scoring 186 points is 2.643 standard deviations away from the mean. A positive value of z means that that the value is above (or to the right of) the mean, which was given in the problem: μ=149 points in the game. • Suppose X∼N(18,2), and x=22. Find and interpret the zscore of the standardized normal random variable. The z-score when x=22 is . The mean is . This z-score tells you that x=22 is deviations to the right of the mean. standard • Suppose X∼N(12.5,1.5), and x=11. Find and interpret the zscore of the standardized normal random variable. X is a normally distributed random variable with μ=12.5 (mean) and mean) and σ=1.5 [Show More]

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