Question

In the United States, the ages 11 to 55+ of smartphone users approximately follow a normal distribution with an approximate mean of 34.8 years and a standard deviation of 14.1 years. Determine the probability that a randomly selected smartphone users in the age range 11 to 55+ is between 30 and 54 years old.

Answer 1

0.546 is the probability that a randomly selected smartphone users in the age range 11 to 55+ is between 30 and 54 years old.

Explanation:

We are given the following information in the question:

Mean, μ = 34.8 years

Standard Deviation, σ = 14.1 years

We are given that the distribution of ages of smartphone is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P( age range is between 30 and 54 years old)

`P(30 \leq x \leq 54) = P(\displaystyle(30 - 34.8)/(14.1) \leq z \leq \displaystyle(54-34.8)/(14.1)) = P(-0.3404 \leq z \leq 1.3617)\\\\= P(z \leq 1.3617) - P(z < -0.3404)\\= 0.913 - 0.367 = 0.546 = 54.6\%`

`P(30 \leq x \leq 54) = 54.6\%`

0.546 is the probability that a randomly selected smartphone users in the age range 11 to 55+ is between 30 and 54 years old.