a random sample of fortyeight 200meter swims has a mean time

a random sample of forty-eight 200-meter swims has a mean time of 3.22 minutes and standard deviation of 0.09 minute. construct a 95% confidense interval for the population mean time. Interpret the results.

Solution

Solution:

sample mean=x-bar = 3.22
sample standar dsd = 0.09
n = 48
z_c = 1.96 for 95% confidence intreval
margin of error, E = (sd*z_c)/sqrt(n)
= (0.09*1.96)/sqrt(48)
= 0.0255

95% CI = (x-bar - E, x-bar + E)
= (3.22 - 0.0255 , 3.22 + 0.0255 )
= (3.1945, 3.2455)

Given sample mean lies in between confidence interval

3.1945<3.22<3.2455