The Orchard Cafe has found that about 12% of the diners who make reservations don't show...

The Orchard Cafe has found that about 12% of the diners who make reservations don't show up. If 75 reservations have been made, how many diners can be expected to show up? Find the standard deviation of this distrubution.

Expert Solution

Here

probability that a person who made reservation does not show up = 0.12 (12% in decimals = 12/100 = 0.12)

probability that a person who made reservation shows up = total probability - probability that a person who made reservation does not show up

=>probability that a person who made reservation shows up = 1 - 0.12 = 0.88

It is a case of Binomial distribution because the probability of an event is fixed and there are two events only that is a person who made reservation shows up or a person who made reservation does not show up.

n = number of reservations = 75

In Binomial distribution, Mean = np

here p = probability that a person who made reservation shows up = 0.88

p + q = 1 = total probability

q = probability that a person who made reservation does not show up = 0.12

Mean = np = 75 × 0.88 =66

diners can be expected to show up = Mean value = 66

standard deviation of Binomial distribution =

orchestra answered 1 year ago

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