Question

Attendances at a high school's basketball games were recorded and found to have a sample mean and variance of 490 and 36, respectively. Calculate x ± s,x ± 2s, and x ± 3s.

Answer 1

a)
`x \pm s = 484 \& 496`

b)
`x \pm 2s = 478 \& 502`

c)
`x \pm 3s= 472 \& 508`

Explanation:

sample mean
`(\overline{x})=490`

sample variance
`(\overline{s}^2)=36`

sample standard deviation
`(\overline{s}^2)` will be the square root of the sample variance:

`\overline{s} = √(36) = 6`

Now we'll do our calculations:

a)
`x \pm s`

`x \pm s = 490 \pm 6`

`490 - 6\,\&\, 490 + 6`

`484 \& 496`

b)
`x \pm 2s`

`x \pm 2s = 490 \pm 2(6)`

`490 - 12\,\&\, 490 + 12`

`478 \& 502`

c)
`x \pm 3s`

`x \pm 3s = 490 \pm 3(6)`

`490 - 18\,\&\, 490 + 18`

`472 \& 508`