91Ó°ÊÓ

82. Would you be surprised, based upon numerical calculations, if the sample average wait time (in minutes) for 100 riders was less than 30 minutes?

a. yes

b. no

c. There is not enough information.

Find the probability that the average price for $30$gas stations is less than $\$4.55$.

a.$0.6554$

b. $0.3446$

c.$0.0142$

d.$0.9858$

e.$0$

Suppose in a local Kindergarten through $12th$grade $(K-12)$school district, $53$percent of the population favor a charter school for grades K through five. A simple random sample of 300 is surveyed. Calculate following using the normal approximation to the binomial distribtion.

a. Find the probability that less than $100$favor a charter school for grades $K$through $5$.

b. Find the probability that $170$or more favor a charter school for grades $K$through $5$.

c. Find the probability that no more than $140$favor a charter school for grades $K$through $5$.

d. Find the probability that there are fewer than $130$that favor a charter school for grades $K$through $5$.

e. Find the probability that exactly $150$favor a charter school for grades $K$through $5$.

If you have access to an appropriate calculator or computer software, try calculating these probabilities using the technology.

Four friends, Janice, Barbara, Kathy and Roberta, decided to carpool together to get to school. Each day the driver would be chosen by randomly selecting one of the four names. They carpool to school for $96$days. Use the normal approximation to the binomial to calculate the following probabilities. Round the standard deviation to four decimal places.

a. Find the probability that Janice is the driver at most$20$days.

b. Find the probability that Roberta is the driver more than $16$days.

c. Find the probability that Barbara drives exactly $24$ of those $96$ days.

$X~N(60,9)$. Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let $\mathrm{Î\pounds }X$be the random variable of sums. For parts, c through f, sketch the graph, shade the region, label and scale the horizontal axis for $\stackrel{-}{X}$, and find the probability.

a. Sketch the distributions of X and $\stackrel{-}{X}$on the same graph.

b. $\stackrel{-}{X}~$

c. $P(\stackrel{-}{X}<60)=$

d. Find the 30th percentile for the mean.

e. $P(56<\stackrel{-}{X}<62)$

f. $P(18<\stackrel{-}{X}<58)=$

g. $\mathrm{Î\pounds ³Ý}~$

h. Find the minimum value for the upper quartile for the sum.

i. $$P(1,400<\mathrm{Î\pounds ³Ý}<1,550)=$

Suppose that the length of research papers is uniformly distributed from ten to \(25\) pages. We survey a class in which \(55\) research papers were turned in to a professor. The \(55\) research papers are considered a random collection of all papers. We are interested in the average length of the research papers.

a. In words, \(X= \)

b. \(X= ( , )\)

c. \(\mu_{x}= \)

Salaries for teachers in a particular elementary school district are normally distributed with a mean of$\backslash (44,000$and a standard deviation of $\backslash )6,500$. We randomly survey ten teachers from that district.

a. Find the$90th$percentile for an individual teacher’s salary.

b. Find the $90th$percentile for the average teacher’s salary.

The average length of a maternity stay in a U.S. hospital is said to be \(2.4\) days with a standard deviation of \(0.9\) days. We randomly survey \(80\) women who recently bore children in a U.S. hospital.

a. In words, \(X= \)

b. In words, \(\bar{X}= \)

c. \(\bar{X} ( , )\)

NeverReady batteries has engineered a newer, longer lasting AAA battery. The company claims this battery has an average life span of $17$ hours with a standard deviation of $0.8$ hours. Your statistics class questions this claim. As a class, you randomly select $30$ batteries and find that the sample mean life span is $16.7$ hours. If the process is working properly, what is the probability of getting a random sample of $30$ batteries in which the sample mean lifetime is $16.7$ hours or less? Is the company’s claim reasonable?

Men have an average weight of $172$pounds with a standard deviation of $29$pounds.

a. Find the probability that $20$randomly selected men will have a sum weight greater than $3600$lbs.

b. If $20$ men have a sum weight greater than $3500$lbs, then their total weight exceeds the safety limits for water taxis. Based on (a), is this a safety concern? Explain.