91Ó°ÊÓ

If a set of observations is normally distributed, what percent of these differ from the mean by (a) more than \(1.3 \sigma ?\) (b) less than \(0.52 \mathrm{cr} ?\)

The IQs of 600 applicants of a certain college are approximately normally distributed with a mean of 115 and a standard deviation of \(12 .\) If the college requires an IQ of at least, \(95,\) how many of these students will be rejected on this basis regardless of their other qualifications?

Given a continuous uniform distribution, show that (a) \(\mu=\frac{A+B}{2},\) and (b) \(\sigma^{2}-\frac{(B-\lambda)^{2}}{12}\)

The daily amount of coffee, in liters, dispensed by a machine located in an airport, lobby is a random variable \(X\) having a continuous uniform distribution with \(A=7\) and \(B=10 .\) Find the probability that on a given day the amount of coffee dispensed by this machine will be (a) at most 8.8 liters; (b) more than 7.4 liters but less than 9.5 liters; (c) at least 8.5 liters.

A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution. (a) What is the probability that the individual waits more than 7 minutes? (b) What is the probability that the individual waits between 2 and 7 minutes?

A coin is tossed 400 times. Use the normal-curve approximation to find the probability of obtaining (a) between 185 and 210 heads inclusive; (b) exactly 205 heads; (c) less than 176 or more than 227 heads.

A process for manufacturing an electronic component is \(1 \%\) defective. A quality control plan is to select 100 items from the process, and if none are defective, the process continues. Use the normal approximation to the binomial to find (a) the probability that the process continues for the sampling plan described; (b) the probability that the process continues even if the process has gone bad (i.e., if the frequency of defective components has shifted to \(5.0 \%\) defective ).

A process yields \(10 \%\) defective items. If 100 items are randomly selected from the process, what is the probability that the number of defectives (a) exceeds \(13 ?\) (b) is less than \(8 ?\)

The probability that a patient recovers from a delicate heart operation is \(0.9 .\) Of the next 100 patients having this operation, what is the probability that (a) between 84 and 95 inclusive survive? (b) fewer than 86 survive?

If \(20 \%\) of the residents in a U.S. city prefer a white telephone over any other color available, what is the probability that among the next 1000 telephones installed in that city (a) between 170 and 185 inclusive will be white? (b) at least 210 but not more than 225 will be white?