In Melanie's Styling Salon, the time to complete a simple haircut is normally distributed with a mean of 25 minutes and a standa

Answer:

b) falls between 18.4 and 31.6 minutes.

Step-by-step explanation:

Problems involving normally distributed samples can be tackled using the z-score formula.

In any set with a mean and standard deviation , the z-score for a measurement X is calculated as follows:

The Z-score indicates how many standard deviations an observation diverges from the mean. After determining the Z-score, consulting the z-score table provides the associated p-value. This p-value represents the likelihood of observing a measure less than X, i.e., the percentile of X. Subtracting the p-value from 1 yields the probability of observing a measure greater than X.

In this question, we find that:

To cover the Middle 90%

The lower limit is determined as the value of X when Z corresponds to a p-value of 0.5 - 0.9/2 = 0.05.

The upper limit corresponds to the value of X when Z has a p-value of 0.5 + 0.9/2 = 0.95.

X when Z = -1.645

X when Z = 1.645

Thus, the correct assessment is:

b) between 18.4 and 31.6 minutes.