Question

Suppose the heights of units of product from a company follow a normal distribution with an unknown mean and standard deviation. They collect a sample of 49 units and find a sample mean height of 23.5 inches and a sample standard deviation of 2 inches. Calculate a 99.7% tolerance interval. Enter your lower bound below. Do not round your answer

Answer 1

Solution :

Given that,

= 23.5

s = 2

n = 49

Degrees of freedom = df = n - 1 = 49 - 1 = 48

At 99.7% confidence level the t is ,

= 1 - 99.7% = 1 - 0.997 = 0.003

/ 2 = 0.003 / 2 = 0.0015

t /2,df = t0.0015,48 =3.127

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

= 3.127 * (2 / 49)

= 0.9

Margin of error = 0.9

The 99.7% confidence interval estimate of the population mean is,

- E

23.5 -0.9

= 22.6

lower bound = 22.6