Question

An insurance company claims that in the population of homeowners, the mean annual loss from fire is u-$5000 with a standard deviation of o-$250

distribution of loss is strongly right-skewed: Many policies have $0 loss, but a few have large losses.
If we create a sampling distribution with a sample of 64 homeowners, what is the z-score that corresponds to a sample average of $5100?
Round to four decimals
Type your answer.
1 point

Answer 1

To find the z-score, we use the formula:

z = (x - mu) / (sigma / sqrt(n))

where:

x = sample mean = $5100

mu = population mean = $5000

sigma = population standard deviation = $250

n = sample size = 64

Substituting the values, we get:

z = (5100 - 5000) / (250 / sqrt(64))

z = 2.56

Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).

Explanation:

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