Question

the orchard cafe has found that about 15% of the diners who make reservations don't show up. if 90 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.)

Answer 1

Out of 90 reservation made, 77 diners are expected to show up. And the standard deviation of this binomial distribution is 3.39

We have been given that

   Percentage of people who make reservation and didn’t show up = 15%                       = 0.15

   Number of reservation made = 90

 Now we have to calculate number of people expected to show up that is we have to calculate mean. As this a binomial distribution in which we have been given

    n = 90   and q = 0.15  

Thus, µ = np = 90*(1-0.15) = 90*0.85

          µ = 76.5 ≈ 77

Thus it is expected to have 77 diners to show up.

Now standard deviation is given as:

σ = √npq

σ = √90*0.15*0.85

σ = 3.39

Hence the standard deviation is 3.39

Learn more about binomial distribution here : brainly.com/question/25992005

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