Question

In a certain region, suppose the ages of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 39.9 years and 9.1 years, respectively. Determine the probability that a random smartphone user is at most 48 years old. • Round your answer to four decimal places.

Answer 1

Answer:

0.8133.

Step-by-step explanation:

We have been given that the ages of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 39.9 years and 9.1 years, respectively.

First of all, we will use z-score formula to find z-score of 48.

$z=\frac{x-\mu}{\sigma}$, where,

$z$ = z-score,

$x$ = Sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

Substitute the given values:

$z=\frac{48-39.9}{9.1}$

$z=\frac{8.1}{9.1}$

$z=0.89$

Now, we will need to find the probability of z-score less than or equal to 0.89 as:

$P(z\leq 0.89)$

Using normal distribution table, we will get:

$P(z\leq 0.89)=0.81327$

$P(z\leq 0.89)\approx 0.8133$

Therefore, the probability that  a random smartphone user is at most 48 years old would be 0.8133.