# In a manufacturing process, a random sample of 36 manufactured bolts has a mean length of 3 cm...

## Question:

In a manufacturing process, a random sample of 36 manufactured bolts has a mean length of 3 cm with a standard deviation of 0.3 cm. What is the 99 percent confidence interval for the true mean length of the manufactured bolt?

A). 2.802 to 3.198

B). 2.228 to 3.772

C). 2.864 to 3.136

D). 2.902 to 3.098

E). 2.884 to 3.117

## Confidence Interval:

In this question, we will use the t distribution to calculate and construct the 99% confidence interval for the true mean length of the manufactured bolt. The t distribution is a sampling distribution with (n-1) degree of freedom.

Given that,

• Sample size, {eq}n = 36 {/eq}
• Mean, {eq}\bar{x} = 3 {/eq}
• Standard deviation, {eq}s=0.3 {/eq}

Degree of freedom, {eq}n-1 = 36-1 = 35 {/eq}

The 99% confidence interval for the population mean is defined as:

{eq}\bar{x} \pm t_{0.01/2}\times \frac{s}{\sqrt{n}} {/eq}

Excel function for the confidence coefficient:

=TINV(0.01,35)

Now,

{eq}3 \pm 2.724\times \frac{0.3}{\sqrt{36}}\\ 2.864 < \mu < 3.136 {/eq}

Therefore, Option (C) is correct.