Question

QUESTION 39.1 POINT

Answer 1

Answer:

The Z-score when x = 76 is of -0.125, which tells you that x = 76 is 0.125 standard deviations to the left of the mean.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

X ~ N(77,8).

This means that $\mu = 77, \sigma = 8$

Z-score when X = 76:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{76 - 77}{8}$

$Z = -0.125$

Negative means that its to the left of the mean.

The Z-score when x = 76 is of -0.125, which tells you that x = 76 is 0.125 standard deviations to the left of the mean.