MATH 225N Week 5 Understanding Normal Distribution; complete solutions guide "A" 2024

MATH 225N Week 5 Understanding Normal Distribution; complete solutions guide "A" 2024• 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 ofpoints per bowling game. Then X∼N(149,14). Suppose Lexie scores 186 points in the game on Tuesday. The z-score when x = 186 is - no response given. The mean is - no response given. This z-score tells you that x = 186 is - no response given standarddeviations 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 (tothe 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 z- score of thestandardized normal random variable.