Suppose Kristen is researching failures in the restaurant business. In the city where she lives, the probability that an independent restaurant will fail in the first year is 43 % . 43%. She obtains a random sample of 66 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. What are the mean and standard deviation of the number of restaurants that failed within a year

The probability of occurrence is constant. The events(failing of restaurants) are independent. Number of trials if fixed and there are only two possible outcomes i.e. either restaurant failed or not failed.

This scenario satisfies all the conditions of a Binomial experiment setting. So, we will use Binomial Experiment to answer the questions.

The formula to calculate the Mean of Binomial Distribution is:

Mean = u = np

Here, n is the number of trials, which is 66 in this case. So,

Mean = u = 66 x 0.43 = 28.38

Standard Deviation of a Binomial Distribution is calculated as:

[tex]s=\sqrt{np(1-p)} \\\\ s=\sqrt{66 \times 0.43 \times (1-0.43)}\\\\ s=\sqrt{16.1766}\\\\ s=4.02[/tex]

andromache andromache · Answer 2 · 2022-03-01T12:07:01+01:00

The mean and standard deviation of the number of restaurants that failed within a year is 28.38 and 4.02.

Calculation of the mean and standard deviation:

Since the probability that an independent restaurant will fail in the first year is 43 % . 43%. She obtains a random sample of 66 independent restaurants

Now

The mean is

Mean = u = 66 (0.43) = 28.38

And, the standard deviation is

[tex]= \sqrt{66 \times 0.43 \times (1 - 43\%)[/tex]

= 4.02

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