Annie averages 23 points per basketball game with a standard deviation of 4 points. Suppose Annie's points per basketball game are normally distributed. Let X = the number of points per basketball game. Then X ~ N(23,4) Provide your answer below: The mean is Suppose Annie scores 34 points in the game on Sunday. The z-score when x-34 is This z-score tells you that x=34 is standard deviations to the right of the mean.

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

Given:

Annie averages 23 points per basketball game with a standard deviation of 4 points.

Suppose Annie's points per basketball game are normally distributed.

Let X = the number of points per basketball game.

By Notation,

X ~ N(23,4) means E(X) = 23, SD(X) = 4

Mean = 23 , Standard deviation = 4

So,

[tex]Z_s_c_o_r_e = \frac{Value - Mean}{Sd}\\Z_s_c_o_r_e = \frac{34-23}{4}\\ = \frac{11}{4} Z_s_c_o_r_e = 2.75[/tex]

mean = 23

This z-score tells you x = 34 is 2.75 standard deviations to the right of mean.

Hence, this z-score tells you x = 34 is 2.75 standard deviations to the right of mean. And the mean is 23.

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