Find the standard deviation of this distribution.

Question

The Orchard Cafe has found that about 20% of the diners who make reservations don't show up. If 71 reservations have been made, how many diners can be expected to show up? Find the standard deviation of this distribution. (Round your answers to two decimal places)

𝜇 =

𝜎 =

Answer 1

The mean is equal to the product of the sample size (N) and the probability (P) of a diner showing up.

So in this case N = 71 and the P = .80

The mean is equal to 71 X .80 = 56.8

57 diners are expected to show up

The standard deviation is equal to the square root of the product of the sample size (N), the probability of a diner showing up (P), and the probability of error (E), or the probability of a diner not showing up

71 X .80 X .20 = 11.36

And the square root of that is equal to 3.37

The standard deviation is about 3 diners