Question

The results of a sample of 372 subscribers to Wired magazine shows the time spent using the Internet during the week. Previous surveys have revealed that the population standard deviation is 10.95 hours.

What is the probability that another sample of 372 subscribers spends less than 19.00 hours per week using the Internet?

Descriptive statistics
	Column1
count	372
mean	18.54
sample standard deviation	10.81
sample variance	116.75
minimum	2
maximum	38
range	36
standard error of the mean	0.56
confidence interval 95.% lower	17.45
confidence interval 95.% upper	19.64
margin of error	1.10
z	1.96

Answer 1

Here, μ = 18.54, σ = 0.5677 and x = 19. We need to compute P(X <= 19). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (19 - 18.54)/0.5677 = 0.81

Therefore,
P(X <= 19) = P(z <= (19 - 18.54)/0.5677)
= P(z <= 0.81)
= 0.7910