Question

The weights, in pounds, of the cats in an animal adoption center are normally distributed. If a random sample of cats is taken and the confidence interval is (7.9,12.7), what is the margin of error

Answer 1

Answer: 2.4

Explanation:

Given : The weights, in pounds, of the cats in an animal adoption center are normally distributed.

The confidence interval is (7.9,12.7) (1)

Let
`\overline{x}` be the sample mean of the weights, in pounds, of the cats in an animal adoption center.

We know that the confidence interval for population mean is given by :-

`(\overline{x}-E,\overline{x}+E)` (2)

From (1) and (2)

`\overline{x}-E=7.9-------(3)\\\\\overline{x}+E=12.7--------------(4)`

Subtracting (3) from (4), we get

`2E=4.8\\\\\Rightarrow\ E=2.4`

Hence, the margin of error is E = 2.4