# statistics BUS 219/MAT167 Online sections

January 30, 2017

Question
BUS 219/MAT167 Online sections
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The average number of pounds of meat that a person consumes each year is 218.4 pounds. Let the standard deviation = 25 pounds and assume the distribution is approximately normally distributed. Find the probability that a randomly selected person (10 points)
a) Consumes less than 224 pounds per year

b) Consumes between 216 and 220 pounds per year

To help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 5% of students in the district based on a reading exam. The average score on that exam is 122.6 and the standard deviation is 18. Find the cutoff score needed to make a student eligible for the special reading program. (5 points)
Assume that the mean systolic blood pressure of normal adults is 122 milliliters of mercury with a standard deviation of 5.6 milliliters. Assuming a normal distribution, what is the probability that (11 points)
a) An individual teacher will have a pressure between 120 and 121.8 milliliters?

b) That a sample of 30 adults will have a pressure between 120 and 121.8 milliliters?

c) Explain the difference in the answers for parts a and b.

Women make up 24% of the science and engineering workforce. In a random sample of 400 science and engineering employees , what is the probability that(10 points)
a) More than 120 are women?

b) between 70 and 95 are women?

A researcher wishes to estimate the average amount of money that a person spends on lottery tickets per month. A sample of 50 people who play the lottery found a mean of \$19 with a standard deviation of 6.8. Find the 95% confidence interval of the population mean.(5 points)
A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large pizza. How large a sample is needed is she wants to be accurate to within \$0.15 given that a previous study found a standard deviation of \$0.26?(5 points)
A recent study showed that 27 residents of Bowie had lived in their homes an average of 11.2 years. The standard deviation was 2. Find the 99% confidence interval of the true mean.(5 points)
A sample of 12 funeral homes in Ohio found these costs for cremation:
320 152 190 285 570 995

585 820 195 160 590 150

Find the 90% confidence interval for the population mean.(7 points)

In a recent study of 154 households, 54 had air conditioning. Find the 95% confidence interval of the true proportion who have air conditioning.(5 points)
Mr. Hoyack, and Dr. Jensen wish to estimate, within 0.05%, the true proportion of Cochise College students who study at least 3 hours each school night and they want to be 99% confident.(10 points)
a) How large a sample is necessary if a study two years ago showed that 65% of 450 students studied at least 3 hours each school night?

b) If no estimate of the sample proportion is available, how large should the sample be?

Find the 95% confidence interval for the standard deviation of the diameter of oranges if a sample of 47 oranges had a standard deviation of 0.18 inches.(5 points)
Jimmy Stewart, Tucson’s premier weather “guy”, claims that the average of the highest temperatures in the U.S. is 93 degrees. A random sample of 35 cities that have high temperatures has an average of 95.8 degrees with a standard deviation of 4.2. Test Jimmy’s claim at “alpha” = 0.05.(11 points; 3, 2, 3, 1, 2)
Nationwide, the average salary of college graduates is \$39,000. A college placement officer feels that the average is higher for graduates at her college. She surveys 31 graduates and finds an average of \$40,500 with a standard deviation of \$4150. Can her claim be supported at “alpha” = 0.05? What about at “alpha” = 0.01?(11 points; 3, 2, 3, 1, 2)

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