Answer to Question #219968 in Statistics and Probability for darily

Question

A study was conducted in order to determine if any link existed between cellular phone usage and the development of brain cancer. Data from this study indicated that the monthly phone usage for all users is approximately normally distributed with mean 2.4 hours and standard deviation 1.1 hours. Up to how many hours does the lower 80% of the users spend on the phone?

a. 1.82 hours

b. 3.33 hours

c. 1.47 hours

d. 3.12 hours

e. 3.81 hours

Answer 1

Let $X=$ the monthly phone usage in hours: $X\sim(\mu, \sigma^2).$

Given $\mu=2.4\ h, \sigma=1,1\ h.$

$$P(Z<z)=0.8$$

$$z\approx0.841621$$

$$\dfrac{x-2.4}{1.1}\approx0.841621$$

$$x\approx1.1(0.841621)+2.4$$

$$x\approx3.33$$

b. 3.33 hours