Question

A study indicates that​ 18- to​ 24- year olds spend a mean of 140 minutes watching video on their smartphones per month. Assume that the amount of time watching video on a smartphone per month is normally distributed and that the standard deviation is 15 minutes. Complete parts​ (a) through​ (d) below. a. What is the probability that an​ 18- to​ 24-year-old spends less than 120 minutes watching video on his or her smartphone per​ month? The probability that an​ 18- to​ 24-year-old spends less than 120 minutes watching video on his or her smartphone per month is nothing. ​(Round to four decimal places as​ needed.)

Answer 1

Answers:

a) 0.091

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 140 minutes

Standard Deviation, σ = 15 minutes

We are given that the distribution of time watching videos is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(time is less than 120 minutes)

$P(x < 120) = P(z > \displaystyle\frac{120-140}{15}) = P(z \leq -1.3333)$

Calculating the value from the standard normal table we have,

$P(z \leq -1.3333) = 0.091 = 9.1\%\\P( x < 120) = 9.1\%$

The probability that an​ 18- to​ 24-year-old spends less than 120 minutes watching video on his or her smartphone per month is 0.091