Question

question 5
the number of days (x) after mailout it takes a utility company to receive payment for a customers bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days.
about 16% of bills will be received earlier than days after mailout.
question 6
the average time to complete a 10k race for a f runner is 64.61 minutes with a standard deviation of 5.18 minutes. sarah completes her 19 k race in 58.24 minutes. what is sarahs z - score? (round your answer to 2 decimal plac
question 7
the time it takes a surgeon to complete a lapro urgery to remove the gall bladder is normally distributed with a mean of 132.4 min a standard deviation of 15.7 minutes. a patients risk of complications is increased the ne is in surgery. an unusually risky surgery is one that is in the

Explanation:

Step1: Recall z - score property for normal distribution

For a normal distribution, about 16% of the data lies to the left of \(z=- 1\) in the standard - normal distribution (\(Z=\frac{X-\mu}{\sigma}\)).

Step2: Rearrange the z - score formula to solve for \(X\)

We know \(Z=\frac{X - \mu}{\sigma}\), and we want to find \(X\). Rearranging gives \(X=\mu+Z\sigma\). Given \(\mu = 31\) (mean) and \(\sigma = 6\) (standard deviation) and \(Z=-1\).
\[X=31+( - 1)\times6\]
\[X = 31 - 6=25\]

Answer:

25