In a manufacturing process, a random sample of 9 manufactured bolts has a mean length of 3 inches with a variance of .09 and is normally distributed. What is the 90 percent confidence interval for the true mean length of the manufactured bolt

u = (3.1645, 2.8355)

Step-by-step explanation:

Constructing a 90% confidence interval for population mean (u) is given by

u = x + Zα/2 * σ/√n or u = x - Zα/2 * σ/√n

u = population mean

x = sample mean = 3

σ = population standard deviation = √0.09= 0.3

The question gave us variance and standard deviation = √variance.

Zα/2= z score for a two tailed test at level of significance α = 1.645 ( for a 90% confidence level)

For the upper limit

u = 3 + 1.645 * (0.3/√9)

u = 3 + 1.646 * (0.3/3)

u = 3 + 1.645 * (0.1)

u = 3 + 0.1645

u = 3.1645

For lower limit

u = 3 - 1.645 * (0.3/√9)

u = 3 - 1.646 * (0.3/3)

u = 3 - 1.645 * (0.1)

u = 3 - 0.1645

u = 2.8355

Hence the interval for population mean at 95% confidence level is

u = (3.1645, 2.8355)