Respuesta :
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.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z[/tex] = z-score,
[tex]x[/tex] = Sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Substitute the given values:
[tex]z=\frac{48-39.9}{9.1}[/tex]
[tex]z=\frac{8.1}{9.1}[/tex]
[tex]z=0.89[/tex]
Now, we will need to find the probability of z-score less than or equal to 0.89 as:
[tex]P(z\leq 0.89)[/tex]
Using normal distribution table, we will get:
[tex]P(z\leq 0.89)=0.81327[/tex]
[tex]P(z\leq 0.89)\approx 0.8133[/tex]
Therefore, the probability that a random smartphone user is at most 48 years old would be 0.8133.
