Question

The Smith Trucking Company claims that the average weight of its delivery

trucks when fully loaded is 6000 pounds with a standard deviation of 120

pounds. 36 trucks are selected at random and their weights recorded.

Within what limits will the average weights of 90% of the 36 trucks lie?

Answer 1

We have a normal distribution,

$\bar x=6000,\sigma=120, n=36.$

The formula to calculate a confidence interval for a population mean is as follows:

$CI=\bar{x}\pm z\cdot\cfrac{\sigma}{\sqrt{n}},$

where:

• $\bar{x}=6000-$ sample mean
• z- the chosen z-value, for a 90% confidence interval z = 1.645
• $\sigma=120-$ sample standard deviation
• n =36 - sample size.

So,

$CI=6000 \pm 1.645\cdot\cfrac{120}{\sqrt{36}}=\\=6000\pm32.9=(5967.1, 6032.9).$