Answer to Question #176386 in Economics for Farhan Ishraq Abir

Question

A random sample of 20 employees was collected from Brac University, to estimate the average daily time they spent on social media. Suppose that the population times have a normal distribution with a mean of 85 minutes and a standard deviation of 13 minutes. (answer in three decimal places) [5 marks]

a. Find the probability that the sample mean is fewer than 92 minutes?

b. What is the probability that the sample mean is more than 77 minutes and fewer than 90 minutes?

Answer 1

$$z=\frac {92-85}{13}=0.538$$

Using tables p=35%

b.

$$z_1=\frac {77-85}{13}=-0.615$$

$$z_2=\frac {90-85}{13}=0.385$$

$$p=\frac {1}{2}(0.648+0.729)=0.689$$