The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 579 MPa with a standard deviation of 14 MPa.

(a) What is the probability that a randomly chosen sample of glass will break at less than 579 MPa?

(b) More than 590 MPa?

(c) Less than 600 MPa? (Data are from Science 283 [February 26, 1999], p. 1296.)

The length of a certain kind of Colorado brook trout is normally distributed with a mean of 12.5 inches and a standard deviation of 1.2 inches. What minimum size limit should the Department of Natural Resources set if it wishes to allow people to keep 80 percent of the trout they catch?

Vail Resorts pays part-time seasonal employees at ski resorts on an hourly basis. At a certain mountain, the hourly rates have a normal distribution with $\sigma = \$3.00$. If 20 percent of all part- time seasonal employees make more than $13.16 an hour, what is the average hourly pay rate at this mountain?

Most people think of science as being a specific, exact discipline, with a "correct" answer for every problem. Yet you were introduced to the concept of uncertainty in scientific measurements. What is meant by "uncertainty"? How does uncertainty creep into measurements? How is uncertainty indicated in scientific measurements? Can uncertainty ever be completely eliminated in experiments? Explain.

As discussed in the text, Annie Jump Cannon and her colleagues developed our modern system of stellar classification. Why do you think rapid advances in our understanding of stars followed so quickly on the heels of their efforts? What other areas in science have had huge advances in understanding following directly from improved systems of classification?

When confronted with an in-flight medical emergency, pilots and crew can consult staff physicians at MedAire, an emergency facility in Tempe, Arizona. If MedAire is called, there is a 4.8 percent chance that the flight will be diverted for an immediate landing.

(a) If MedAire is called 8,465 times (as it was in 2002), what is the expected number of diversions?

(b) What is the probability of at least 400 diversions?

(c) Fewer than 450 diversions? Show your work carefully. (Data are from Popular Science 263, no. 5 [November 2003], p. 70.)

A box In Ms. Booth's class contains 200 loose white or yellow golf balls. The table below represents the results when 11 students each drew a random sample of the same number of balls, counted the number of yellows, and then returned the sample to the box.

$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline \text{Student} & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {9} & {10} & {11} \\ \hline \text{Proportion of Yellow} & {0.6} & {0.7} & {0.3} & {0.7} & {0.5} & {0.9} & {0.8} & {0.8} & {0.7} & {0.7} & {0.9} \\ \hline \end{array}$$

Construct a box plot to display the data from Ms. Booth's class.

Jim’s systolic blood pressure is a random variable with a mean of 145 mmHg and a standard deviation of 20 mmHg. For Jim’s age group, 140 is the threshold for high blood pressure.

(a) If Jim’s systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 135 or less?

(b) 175 or more?

(c) Between 125 and 165?

(d) Discuss the implications of variability for physicians who are trying to identify patients with high blood pressure.

(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (b) What happens to the standard error each time you quadruple the sample size?

$$\sigma=32, n=64$$

Find the interval $\left[\mu-z \frac{\sigma}{\sqrt{n}}, \mu+z \frac{\sigma}{\sqrt{n}}\right]$ within which $95$ percent of the sample means would be expected to fall, assuming that each sample is from a normal population.

$$\mu=1,000, \sigma=15, n=9$$

If the temperature in degrees Fahrenheit at a certain location is normally distributed with a mean of 68 degrees and a standard deviation of 4 degrees, what is the distribution of the temperature in degrees Celsius at the same location?

The weight of a miniature Tootsie Roll is normally distributed with a mean of 3.30 grams and standard deviation of 0.13 grams.

(a) Within what weight range will the middle 95 percent of all miniature Tootsie Rolls fall?

(b) What is the probability that a randomly chosen miniature Tootsie Roll will weigh more than 3.50 grams? (Data are from a project by MBA student Henry Scussel.)

The average credit card debt for a recent year was $\$ 9205$. Five years earlier the average credit card debt was $\$ 6618$. Assume sample sizes of 35 were used and the population standard deviations of both samples were $\$ 1928$. Is there enough evidence to believe that the average credit card debt has increased? Use $\alpha=0.05$. Give a possible reason as to why or why not the debt was increased.

The cabin of a business jet has a cabin height 5 feet 9 inches high. If a business traveler’s height is N(5'10'', 2.7''), what percentage of the business travelers will have to stoop?