Question

The distribution of wait times for a movie to load on Hulu is normally distributed with a standard deviation of 4.4 seconds. What changes the mean is how long it takes Windows to give the Hulu player priority in the process queue. I want to know the average on my old computer, so I randomly sample it 19 times, and I get an average of 668 seconds. Find a 87% confidence interval for the average time my old computer takes to play a movie on Hulu.
Ues 2 decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 668

sample standard deviation = s = 4.4

sample size = n = 19

Degrees of freedom = df = n - 1 = 18

At 87% confidence level the t is ,

= 1 - 87% = 1 - 0.87 = 0.13

/ 2 = 0.13 / 2 = 0.065

t _/2,df = t_0.065,18 = 1.587

Margin of error = E = t_/2,df * (s /n)

= 1.587 * (4.4 / 19)

= 0.636

The 87% confidence interval estimate of the population mean is,

- E < < + E

668 - 0.636 < < 668 + 0.636

667.364 < < 668.636

A 87% confidence interval for the average time my old computer takes to play a movie on Hulu is,

(667.364 , 668.636)