Question

The Orchard Cafe has found that about 15% of the diners who make reservations don't show up. If 77 reservations have been made, how many diners can be expected to show up? Find the standard deviation of this distribution

Answer 1

65 dinners are expected to show up

The standard deviation of the distribution is 3.13

Explanation:

Given

Proportion = 15%

Population = 77

Required

Expected Number that'll show up

Standard Deviation

If 15% won't show up; then

100% - 15% = 85% will show up

Expected Number, E(x) of Dinner is calculated as thus;

`E(x) = np`

Where
`p = 85\%` (calculated above)

and
`n = 77`

Convert p to decimal

`p = 0.85`

So;

`E(x) = 0.85 * 77`

`E(x) = 65.45`

`E(x) = 65`

65 dinners are expected to show up

Calculating Standard Deviation, SD

Standard Deviation is calculated as;

`SD = √(np(1-p))`

Substitute 0.85 for p and 77 for n

`SD = √(77 * 0.85 * (1-0.85))`

`SD = √(77 * 0.85 * 0.15)`

`SD = √(9.8175)`

`SD = 3.13328900678`

`SD = 3.13` (Approximated)

The standard deviation of the distribution is 3.13