91Ó°ÊÓ

Consider a normal distribution with mean 30 and standard deviation \(2 .\) What is the probability a value selected at random from this distribution is greater than 30 ?

When we use a normal distribution to approximate a binomial distribution, why do we make a continuity correction?

Consider a binomial experiment with 20 trials and probability \(0.45\) of success on a single trial. (a) Use the binomial distribution to find the probability of exactly 10 successes. (b) Use the normal distribution to approximate the probability of exactly 10 successes. (c) Compare the results of parts (a) and (b).

Assume that \(x\) has a normal distribution with the specified mean and standard deviation. Find the indicated probabilities. $$ P(3 \leq x \leq 6) ; \mu=4 ; \sigma=2 $$

Do you try to pad an insurance claim to cover your deductible? About \(40 \%\) of all U.S. adults will try to pad their insurance claims! (Source: Are You Normal?, by Bernice Kanner, St. Martin's Press.) Suppose that you are the director of an insurance adjustment office. Your office has just received 128 insurance claims to be processed in the next few days. What is the probability that (a) half or more of the claims have been padded? (b) fewer than 45 of the claims have been padded? (c) from 40 to 64 of the claims have been padded? (d) more than 80 of the claims have not been padded?

Assuming that the heights of college women are normally distributed with mean 65 inches and standard deviation \(2.5\) inches (based on information from Statistical Abstract of the United States, 112 th Edition), answer the following questions. (Hint: Use Problems 5 and 6 and Figure 6-3.) (a) What percentage of women are taller than 65 inches? (b) What percentage of women are shorter than 65 inches? (c) What percentage of women are between \(62.5\) inches and \(67.5\) inches? (d) What percentage of women are between 60 inches and 70 inches?

Assume that \(x\) has a normal distribution with the specified mean and standard deviation. Find the indicated probabilities. $$ P(50 \leq x \leq 70) ; \mu=40 ; \sigma=15 $$

Assume that \(x\) has a normal distribution with the specified mean and standard deviation. Find the indicated probabilities. $$ P(7 \leq x \leq 9) ; \mu=5 ; \sigma=1.2 $$

What are the chances that a person who is murdered actually knew the murderer? The answer to this question explains why a lot of police detec\mathrm{\\{} ~ t i v e ~ w o r k ~ b e g i n s ~ w i t h ~ r e l a t i v e s ~ a n d ~ f r i e n d s ~ o f ~ t h e ~ v i c t i m ! ~ A b o u t ~ \(64 \%\) of people who are murdered actually knew the person who committed the murder (Chances: Risk and Odds in Everyday Life, by James Burke). Suppose that a detective file in New Orleans has 63 current unsolved murders. What is the probability that (a) at least 35 of the victims knew their murderers? (b) at most 48 of the victims knew their murderers? (c) fewer than 30 victims did \(\underline{n o t}\) know their murderers? (d) more than 20 victims did not know their murderers?

Assume that \(x\) has a normal distribution with the specified mean and standard deviation. Find the indicated probabilities. $$ P(40 \leq x \leq 47) ; \mu=50 ; \sigma=15 $$