A random sample of 64 observations produced a mean value of 86 and standard deviation of 4.5. The 95% confidence interval for the population mean μ is between:.

(84.876, 87.124)

Step-by-step explanation:

Confidence interval for population mean if population standard deviation is unknown:

, where n= sample size

s= sample standard deviation

= sample mean

significance level

= critical-t value

Given:  n= 64

Degree of freedom = n-1 = 63

s= 4.5

= 86

0.05

= 1.9983

Now, the required 95% confidence interval would be:

The 95% confidence interval for the population mean μ is between: (84.876, 87.124)