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: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.Step-by-step explanation:We are given the following information in the question:Mean, μ =  34.8 yearsStandard Deviation, σ = 14.1 yearsWe are given that the distribution of ages of smartphone is a bell shaped distribution that is a normal distribution.Formula:[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]P( age range is between 30 and 54 years old)[tex]P(30 \leq x \leq 54) = P(\displaystyle\frac{30 - 34.8}{14.1} \leq z \leq \displaystyle\frac{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\%[/tex][tex]P(30 \leq x \leq 54) = 54.6\%[/tex]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.