Question

Jerome averages 16 points a game with a standard deviation of 4 points. Suppose Jerome's points per game are normally distributed. Let X = the number of points per game. ThenX~ N(16,4)

Suppose Jerome scores 10 points in the game on standard deviations to the Monday. The z-score when z= 10is_____ This z-score tells you that (right /left) of the mean, z= 10is _______Correctly fill in the blanks in the statement above. Select the correct answer below

a. "Suppose Jerome scores 10 points in the game on Monday. The z-score when z- 10 is z-1.2 This z-score tells you that z 10is-1.2 standard deviations to the left of the mean, 10."

b. "Suppose Jerome scores 10 points in the game on Monday. The 2-score when z you that z 10is 1.2 standard deviations to the right of the mean, 16." 1.2 This -score tells 10 is z

c. "Suppose Jerome scores 10 points in the game on Monday. The 2-score when z you that z 10is 1.5 standard deviations to the left of the mean, 16." 10 is z-1.5. This 2-score tells

d. "Suppose Jerome scores 10 points in the game on Monday. The z-5core when z you that z 10 is 1.5 standard deviations to the right of the mean, 16 1.5. This z-score tells 10is z

e. "Suppose Jerome scores 10 points in the game on Monday. The 2-score when z tells you that z 10is-1.5 standard deviations to the right of the mean, 16."

Answer 1

Jerome's score of 10 points is -1.5 standard deviations to the left of the mean, which is 16 points per game. The z-score of -1.5 indicates the score is below the mean.

Step-by-step explanation:

The z-score is a statistic that tells us how many standard deviations an individual data point (in this case, Jerome's score in a game) is from the mean of the data set. Since Jerome's points per game are normally distributed with a mean of 16 and a standard deviation of 4, and he scored 10 points in Monday’s game, the z-score can be calculated using the formula:

z = (X - μ) / σ

Where X is the individual score, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:

z = (10 - 16) / 4 = -6 / 4 = -1.5

This means Jerome's score is -1.5 standard deviations to the left of the mean. In a normal distribution, scores to the left of the mean are lower than the average, and scores to the right are higher. Hence, the correct option that fills in the blanks is:

c. "Suppose Jerome scores 10 points in the game on Monday. The z-score when x = 10 is z = -1.5. This z-score tells you that x = 10 is 1.5 standard deviations to the left of the mean, 16."