In the United States the ages 13 to 55+ of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 36.9 years and 13.9 years, respectively. What is the probability that a random smartphone user in the age range 13 to 55+ is between 23 and 64.7 years old?

The probability that a random user is between 23 an 64.7 years old is 0.8186

Step-by-step explanation:

1. Relevant data

2. Calculate probabilty.

We want to find the probabilty that a random user is between 23 and 64.7 years old. We can note that condition with the expression:

Replacing

3. Transform x in z-value.

Considering the ages follow a normal distribution, we need to transformx in z-value. We can calculate z with the equation:

Then, probability is given by the equation:

4. Estimate the probabilities in normal distribution table:

The probability that a random user is between 23 an 64.7 years old is 0.8186