Math 04/17

Quiz 2 MA 1510 Student: ___________________________________________________________________________ Each question is worth 2.5 points for a total of 50 points for the quiz.

Show work where applicable. Partial credit is possible. You can submit an Excel spreadsheet if you use

Excel for any of the calculations but be sure you clearly identify the question number with the calculation.

This quiz is given under the honor system. You may use your text and notes, but you may not confer with

anyone to answer the questions.

The quiz must be submitted by 9pm, Wednesday April 23, 2014.

____1. Carlson Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks of the purchase date. Their records reveal that 10% of the diamond wedding rings are returned. Five different customers buy a wedding ring. What is the probability that none of the customers return a ring? A. 0.250

B. 0.073 C. 0.590 D. 0.500

____2. In a large metropolitan area, past records revealed that 30% of all the high school graduates go to college. From

20 graduates selected at random, what is the probability that exactly 8 will go to college? A. 0.114

B. 0.887 C. 0.400 D. 0.231

____3. Chances are 50-50 that a newborn baby will be a girl. For families with five children, what is the probability that

all the children are girls?

A. 0.900 B. 0.031 C. 0.001 D. 0.250

____4. A statistics professor receives an average of five e-mail messages per day from students. Assume the number of

messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have five messages?

A. 0.0067 B. 0.8750 C. 0.1755 D. 1.0000

____5. A total of 60% of the customers of a fast food chain order a hamburger, French fries, and a drink. If a random

sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?

A. 0.000 B. 1.000 C. 0.186 D. 0.403

Problems 6 and 7: A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.

____6. What is the mean number of days absent?

A. 1.00 B. 0.40 C. 0.72 D. 2.5

____7. Given the probability distribution, which of the following predictions is correct?

A. There is a 0.04 probability that an employee will be absent one day per month. B. There is a 0.12 probability that an employee will be absent two days per month. C. There is a 0.50 probability that an employee will be absent 0.72 days per month. D. 60% of the employees will have more than one day absent per month.

____8. What kind of distributions are the binomial and Poisson probability distributions?

A. Discrete B. Continuous C. Both discrete and continuous D. Neither discrete or continuous

____9. Which of the following is correct about a probability distribution?

A. The sum of all possible outcomes must equal 1.0. B. Outcomes must be mutually exclusive. C. The probability of each outcome must be between 0.0 and 1.0 inclusive. D. All apply.

____10. A true/false test consists of six questions. If you guess the answer to each question, what is the probability of

getting all six questions correct?

A. 0.000 B. 0.016 C. 0.062 D. 0.250

____11. The mean amount spent by a family of four on food is $500 per month with a standard deviation of $75.

Assuming that the food costs are normally distributed, what is the probability that a family spends less than $410 per month?

A. 0.1151 B. 0.8750 C. 0.0362 D. 0.2158

____12. The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight

per plant is 15.0 pounds, and the standard deviation of the normally distributed weights is 1.75 pounds. Of the 200 plants in the experiment, how many produced peppers weighing between 13 and 16 pounds?

A. 100 B. 118 C. 197 D. 53

____13. An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a

mean of 75 and a standard deviation of 8. The instructor wants to award the grade of A to the upper 10% of the test grades. To the nearest percent, what is the dividing point between an A and a B grade? A. 95

B. 90 C. 85 D. 80

____14. The distribution of the annual incomes of a group of middle management employees approximated a normal

distribution with a mean of $37,200 and a standard deviation of $800. About 68% of the incomes lie between what two incomes?

A. $36,400 and $38,000 B. $35,600 and $38,800 C. $34,800 and $39,600 D. $30,000 and $40,000

____15. The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a

normal distribution, what test score separates the top 25% of the students from the lower 75% of students?

A. 70.00 B. 74.69 C. 65.31 D. 75.25

____16. As the size of the sample increases, what happens to the shape of the distribution of sample means?

A. It is negatively skewed. B. It is positively skewed. C. It cannot be predicted in advance. D. It approaches a normal distribution.

____ 17. The size of the sampling error is ________.

A. Directly related to the sample size—in other words, the larger the sample size, the larger the sampling error B. Directly related to the population mean—in other words, the larger the mean, the larger the sampling error C. Inversely related to the sample size—in other words, the larger the sample size, the smaller the sampling

error D. Inversely related to the population standard deviation—in other words, the smaller the standard deviation,

the larger the sampling error

____18. Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales

were classified as large; those from $50 to $100 million as medium size; and those between $25 and $50 million, and so on. Samples were then selected from each of these groups. What is this type of sampling called? A. Stratified random sampling

B. Simple random sampling C. Cluster sampling D. Systematic sampling

____19. The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. Based on a large

number of observations, the distribution of trout weights is normally distributed with a mean of 402.7 grams and a standard deviation 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?

A. 1.0 B. 0.5 C. 0.3782 D. 0.0222

____20. The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the probability that the mean of this sample is between 19 hours and 20 hours?

A. 2.00 B. 0.4772 C. -2.00 D. Cannot be calculated based on the given information