Question

The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution = 0.5 and g = 0.289. (a) Let x be the sample mean waiting time for a random sample of 19 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.) HU (b) Answer Part (a) for a random sample of 60 individuals. (Round your answers to three decimal places.)

Answer 1

Solution:

a)

Here , n = 19

$\mu_{\bar x}$ = $\mu$ = 0.5

$\sigma_{\bar x}$ =
ulo
  = 0.289/$\sqrt{}$​19 = 0.066

$\mu_{\bar x}$ = 0.5

$\sigma_{\bar x}$ = 0.066

b)

Here , n = 60

$\mu_{\bar x}$ = $\mu$ = 0.5

$\sigma_{\bar x}$ =
ulo
  = 0.289/$\sqrt{}$​60 = 0.037

$\mu_{\bar x}$ = 0.5

$\sigma_{\bar x}$ = 0.037