A rainstorm in Portland, Oregon, wiped out the electricity in 5% of the households in the city. Suppose that a random sample of 50 Portland households is taken after the rainstorm. Answer the following. (If necessary, consult a list of formulas.) (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.

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### Problem Description
A rainstorm in Portland, Oregon, wiped out the electricity in 5% of the households in the city. Suppose that a random sample of 50 Portland households is taken after the rainstorm.

Answer the following questions:

*(If necessary, consult a [list of formulas](#).)*

**(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.

**Answer:**
[ ]

**(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:**
[ ]

### Explanation
For part (a), you need to calculate the expected number of households that lost electricity. This can be found by determining the mean of the binomial distribution, which is \( E(X) = np \).

For part (b), you should calculate the standard deviation of the binomial distribution, given by \( \sigma = \sqrt{np(1-p)} \).

Use \( n = 50 \) (sample size) and \( p = 0.05 \) (probability of a household losing electricity) for your calculations.
Transcribed Image Text:### Problem Description A rainstorm in Portland, Oregon, wiped out the electricity in 5% of the households in the city. Suppose that a random sample of 50 Portland households is taken after the rainstorm. Answer the following questions: *(If necessary, consult a [list of formulas](#).)* **(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. **Answer:** [ ] **(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:** [ ] ### Explanation For part (a), you need to calculate the expected number of households that lost electricity. This can be found by determining the mean of the binomial distribution, which is \( E(X) = np \). For part (b), you should calculate the standard deviation of the binomial distribution, given by \( \sigma = \sqrt{np(1-p)} \). Use \( n = 50 \) (sample size) and \( p = 0.05 \) (probability of a household losing electricity) for your calculations.
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