Question

A rainstorm in Portland, Oregon, wiped out the electricity in 10% of the households in the city. Suppose that a random sample of 50 Portland households is taken after the rainstorm.Answer the following.(a)Estimate the number of households in the sample that lost electricity by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.(b)Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

Answer 1

Question A:

`\begin{gathered} Mean=np \\ where, \\ n=\text{ Number of sample values} \\ p=\text{ Probability of mean} \\ \\ n=50 \\ p=10\%=(10)/(100) \\ \\ \therefore Mean=50*(10)/(100)=5 \end{gathered}`

- The number of households in the sample that lost electricity is 5

Question B:

`\begin{gathered} \sigma=√(npq) \\ where, \\ \sigma=\text{ Standard deviation} \\ n=\text{ Number of data points in the sample} \\ p=\text{ Probability of obtaining the mean} \\ q=\text{ Probability of NOT}obtaining\text{ the mean}=1-p \\ \\ n=50 \\ p=10\%=0.1 \\ q=1-0.1=0.9 \\ \\ \sigma=√(50*0.1*0.9) \\ \sigma=2.121320343...\approx2.121 \end{gathered}`

- The standard deviation is 2.121

Final answers

- The number of households in the sample that lost electricity is 5

- The standard deviation is 2.121