A company developing a new cellular phone plan intends to market their new phone to customers who use text and social media often. In a marketing survey, they find that customers between age 18 and 34 years send an average of 48 texts per day with a standard deviation of 12. The number of texts sent per day are normally distributed. Required:
a. A customer who sends 78 messages per day would correspond to what percentile?
b. A customer who sends 78 messages per day would be at th percentile.

A customer who sends 78 messages per day would be at 99.38th percentile.

Step-by-step explanation:

Normal Probability Distribution:

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

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

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.

Average of 48 texts per day with a standard deviation of 12.

This means that

a. A customer who sends 78 messages per day would correspond to what percentile?

The percentile is the p-value of Z when X = 78. So

has a p-value of 0.9938.

0.9938*100% = 99.38%.

A customer who sends 78 messages per day would be at 99.38th percentile.

14

step-by-step explanation:

14 x 3 = 42