STAT 200 Homework

76. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.

a.       If X = distance in feet for a fly ball, then X ~ _____(_____,_____)

b.      If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.

c.       Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.

106. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours.

a.       i)

ii)

iii) n =

iv) n-1 =

b.      Define the random variables X and X ¯ in words.

c.       Which distribution should you use for this problem? Explain your choice.

d.      Construct a 95% confidence interval for the population mean time wasted.

i.                    State the confidence interval.

ii.                  Sketch the graph.

iii.                Calculate the error bound.

e.       Explain in a complete sentence what the confidence interval means.

71. Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the Type I error is:

a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher

b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher

102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance.