91Ó°ÊÓ

In a normal distribution, what is the Z-score equivalent of the median? What is the \(Z\) score above which only 16 percent of the distribution lies? What percentage of the scores lie below a \(Z\) score of \(+2.0 ?\).

If \(\mathrm{X}\) has a normal distribution with mean 9 and standard deviation 3, find \(\mathrm{P}(5<\mathrm{X}<11)\).

An electrical firm manufactures light bulbs that have a lifetime that is normally distributed with a mean of 800 hours and a standard deviation of 40 hours. Of 100 bulbs, about how many will have lifetimes between 778 and 834 hours?

The demand for meat at a grocery store during any week is approximately normally distributed with a mean demand of \(5000 \mathrm{lb}\) s and a standard deviation of \(300 \mathrm{lbs}\). (a) If the store has 5300 lbs of meat in stock, what is the probability that it is overstocked? (b) How much meat should the store have in stock per week so as to not run short more than 10 percent of the time?

The life of a machine is normally distributed with a mean of 3000 hours. From past experience, \(50 \%\) of these machine last less than 2632 or more than 3368 hours. What is the standard deviation of the lifetime of a machine?

A teacher decides that the top 10 percent of students should receive A's and the next 25 percent B's. If the test scores are normally distributed with mean 70 and standard deviation of 10 , find the scores that should be assigned A's and B's.

The IQs of the army recruits in a given year are normally distributed with \(\mu=110\) and \(\sigma=8\). The army wants to give special training to the \(10 \%\) of those recruits with the highest IQ scores. What is the lowest IQ score acceptable for this special training?

Let \(\mathrm{X}\) be a normally distributed random variable representing the hourly wage in a certain craft. The mean of the hourly wage is \(\$ 4.25\) and the standard deviation is \(\$ .75\). (a) What percentage of workers receive hourly wages between \(\$ 3.50\) and \(\$ 4.90 ?\) (b) What hourly wage represents the 95 th percentile?

The records of a large university show that \(40 \%\) of the student body are classified as freshmen. A random sample of 50 students is selected. Find (a) the expected number of freshmen in the sample, (b) the standard error of the number of freshmen in the sample, (c) the probability that more than \(45 \%\) are freshmen.

The receiving department of a large television manufacturer uses the following rule in deciding whether to accept or reject a shipment of 100,000 small parts shipped every week by a supplier: Select a sample of 400 parts from each lot received. If \(3 \%\) or more of the selected parts are defective, reject the entire lot; if the proportion of defectives is less than \(3 \%\) accept the lot. What is the probability of rejecting a lot that actually contains \(2 \%\) defectives?