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ZanzabumX [31]
3 years ago
9

The Orchard Cafe has found that about 3% of the diners who make reservations don't show up. If 83 reservations have been made, h

ow many diners can be expected to show up? Find the standard deviation of this distribution. (Round your answers to two decimal places.) μ = σ =
Mathematics
1 answer:
daser333 [38]3 years ago
6 0

Answer:

\mu = 80.51\\\sigma = 1.56

Step-by-step explanation:

We are given the following information in the question:

Percentage of of the diners who make reservations don't show up = 3%

Number of reservations = 83

Thus, we are given a binomial distribution with n = 83 and p = 0.97

X\sim \text{ Binom}(p = 0.97, n = 83)

\mu = np = (83)(0.97) = 80.51

Around 81 people  can be expected to show up.

\sigma = \sqrt{np(1-p)} = \sqrt{(83)(0.97)(1-0.97)} = 1.5541 \approx 1.56

The standard deviation of this distribution is 1.56

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