Question

The mean of a certain set of measurements is 27 with a standard deviation of 14. The distribution of the

Answer 1

Answer:

Exactly 16%.

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.

The mean of a certain set of measurements is 27 with a standard deviation of 14.

This means that $\mu = 27, \sigma = 14$

The proportion of measurements that is less  than 13 is

This is the p-value of Z when X = 13, so:

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

$Z = \frac{13 - 27}{14}$

$Z = -1$

$Z = -1$ has a p-value of 0.16, and thus, the probability is: Exactly 16%.