Question

In a sample of 66 cabinets, the average height was found to be 36.5in. with a variance of 1.7. Give a point estimate for the population standard deviation of the height of the cabinets. Round your answer to two decimal places, if necessary.

Answer 1

Answer: 1.30 in.

Explanation:

Let x denotes the height of cabinets.

We are given that ,

In a sample of 66 cabinets, the average height was found to be 36.5 in. with a variance of 1.7.

i.e. sample mean =
`\overline{x}=36.5\ in.`

Sample variance =
`s^2=1.7\ in`.

Since standard deviation is the square root of variance.

i.e. Sample standard deviation :
`s=√(s^2)=√(1.7)\\\\=1.30384048104\approx1.30\ in`

Since the sample standard deviation(s) is the best point-estimate of the population standard deviation
`(\sigma)` .

Then, a point estimate for the population standard deviation
`(\sigma)` of the height of the cabinets.= 1.30 in.