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. According to a study done by researchers at Georgetown University, recent college graduates who majored in architecture have the highest unemploy- ment rate, at 13.9%. Arts majors are next, with an 11.1% unemployment rate for recent graduates (source: Georgetown Center on Education and the Workforce). Recent graduates are defined as eligible workers between the ages of 22 and 26. In a random sample of 200 recent architecture graduates, compute the a. expected number of grads who are unemployed. b. variance of the random variable "number of grads who are unemployed

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Answer:

The mean is 27.8

The required variance is 23.9358

Step-by-step explanation:

Consider the provided information.

Here the random sample size, n = 200

Unemployment rate is 13.9% = p = 0.139

Part (a) expected number of grads who are unemployed.

[tex]Mean = np\\Mean = 200\times 0.139\\Mean = 27.8[/tex]

Hence, the mean is 27.8

Part (b) variance of the random variable "number of grads who are unemployed.

[tex]Variance = np(1-p)\\Variance = 200\times 0.139(1-0.139)\\Variance = 27.8(0.861)\\Variance = 23.9358[/tex]

Hence, the required variance is 23.9358

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