A rainstorm in Portland Oregon wiped out the electricity in

A rainstorm in Portland, Oregon, wiped out the electricity in 7% of the households in the city. Suppose that a random sample of 70 Portland households is taken after the rainstorm.

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.

Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

Solution

A rainstorm in Portland, Oregon, wiped out the electricity in 7% of the households in the city. Suppose that a random sample of 70 Portland households is taken after the rainstorm.

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.

Binomial distribution used.

n=70

p=0.07

Expectation = np = 4.9

Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

Variance = np(1 - p) = 4.557

Standard deviation = 2.13471

Standard deviation = 2.135   ( three decimals)