# Mathematics

BUS216 Exam #3 Review – SP14

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1. In order to have the standard error of the mean be 12, one would need to take _______ samples from a normally distributed population with a standard deviation of 48.

2. The average price of cell phones manufactured by Ahmadi, Inc. is $98 with a standard deviation of $12. Furthermore, it is known that the prices of the cell phones manufactured by Ahmadi are normally distributed.

a. What percentage of cell phones produced by Ahmadi, Inc. will have prices of at least $120.20?

b. Cell phones with prices of at least 81.80 will get a free gift. What percentage of the cell phones will be eligible for the free gift?

c. What are the minimum and the maximum values of the middle 95% of cell phone prices?

d. If 7,218 of the Ahmadi cell phones were priced at least $119.00, how many cell phones were produced by Ahmadi, Inc.?

3. A manufacturing process produces items whose weights are normally

distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.

4. Catherine Chao, Director of Marketing Research, needs a sample of Kansas City households to participate in the testing of a new toothpaste package. 40% of the households in Kansas City prefer the new package. Catherine conducts a random sample of 300 households in Kansas City asking them whether or not they prefer the new packing. What is probability that in Catherine’s random sample of 300 households more than 135 prefer the new package

5. MNM Corporation gives each of its employees an aptitude test. The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. A simple random sample of 25 is taken from a population.

(a) What is the probability that the average aptitude test in the sample will be

between 70.14 and 82.14?

(b) What is the probability that the average aptitude test in the sample will be greater than 82.68?

6. A professor at a local university noted that the grades of her students were

normally distributed with a mean of 78 and a standard deviation of 10. a) The professor has informed us that 16.6 percent of her students received

grades of A. What is the minimum score needed to receive a grade of A?

BUS216 Exam #3 Review – SP14

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b) If 12.1 percent of her students failed the course and received F’s, what was

the maximum score among those who received an F?

c) If 33 percent of the students received grades of B or better (i.e., A’s and B’s), what is the minimum score of those who received a B?

7. .A large disaster cleaning company estimates that 30% of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that is has contracted; find the probability that x (number of jobs finished on time) is within one standard deviation of the mean. 0.6826

8. The length of time patients must wait to see a doctor in a local clinic is uniformly distributed between 15 minutes and 2 1/2 hours. a. What is the probability that a patient would have to wait between ¾ of an

hour and 2 hours?

b. Calculate the probability that a patient would have to wait over 2 hours. .222 9. X is a normally distributed random variable with a mean of 8 and a standard

deviation of 4.0. Find the value of X for which 70.54% of the area under the distribution curve lies to the right of it. (Note: the diagram is not necessarily to scale.)

BUS216 Exam #3 Review – SP14

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10. The average age of vehicles registered in the United States is 96 months.

Assume the population is normally distributed with a standard deviation of 15 months. Find the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months?

11. A survey of 250 lobster fishermen found that they catch an average of 32.0 pounds of lobster per day with a standard deviation of 4.0 pounds. If a random sample of 36 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds? Assume the distribution of the weights of lobster is normal.

12. DRUGS R US” is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally distributed.

a) What percentage of all bottles produced contains more than

6.51 ounces of vitamins? b) What percentage of all bottles produced contains less than

5.415 ounces? c) What percentage of bottles produced contains between 5.46 to

6.495 ounces d) Ninety-five percent of the bottles will contain at least how

many ounces? e) What percentage of the bottles contains between 6.3 and 6.6

ounces? 13.59%