# statistics midterm exam ch 1 - 6

**work solutions**

**Exam 2**

**Ch.1 to Ch.6**

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Use the following scenario for the next 3 questions. Suppose that monthly sales volume for a product is normally distributed, with a mean of 500 units and a standard deviation of 50 units. If x denotes the number of units sold in a month, what are the following probabilities:

1) P(x < 450)

2) P(x > 600)

3) P(400 < x < 450)

The next 2 questions refer to the following situation. Between the hours of 1:00 and 5:00 PM the average number of phone calls per minute on a cell phone tower is 2.5.

4) What is the probability that during one particular minute there will be more than 6 phone calls?

5) What is the probability that during one particular minute there will be less than 5 phone calls?

The next 2 questions refer to the following scenario. Consider an experiment of flipping a fair coin 50 times. Assign a random variable x, where the value of x is equal to the number of heads observed in the flips.

6) What is the probability of observing 30 or more heads in 50 flips?

7) What is the probability of observing more than 35 **tails** in 50 flips?

Use the following scenario to answer the next 3 questions. Suppose a student in Business Statistics has no been attending class this quarter but decides to take the exam anyway. If he randomly guesses on each of the 20 questions, then he has a 1 out of 5 chance of getting a correct answer, since it is multiple choice exam with choices a, b, c, d, or e.

8) How many questions should the student expect to get correct on this exam?

9) What is the probability that the student will get a “C” or better, which is 14 or more correct?

10) What is the probability that the student will score lower than a “C” (13 or less correct)?

Use the following scenario to answer the next 5 questions. Millions of Americans are subjected to drug testing in the workplace. The tests are not always reliable. A false positive rate of 5% is considered to be a conservative estimate. Suppose that there are 20 employees in your company, which tests its workers weekly.

11) What is the probability of no false-positives for this week’s test?

12) What is the probability of at least 1 false-positive for this week’s tests?

13) What is the likelihood that the test will give 5 to 10 false positives?

14) What is the chance of at most 3 false positives?

15) How many false positives should the company expect?

The next three questions refer to the following situation. Data from previous years reveal that the distribution if first exam scores in an introductory statistics class is approximately normal with a mean of 72 and a standard deviation of 12.

16) Given that the passing score is 65, approximately what percentage of students passes the first exam?

17) What is the probability that the student will score an “A” on the exam? (A score of 90 or more)

18) The middle 95% of the scores will tend to fall between _________ and ________.

19) Two coins are tossed, at the same time, find the probability that two heads are obtained.

a. ½

b. ¼

c. ¾

d.

20) Two dice are rolled, at the same time, find the probability that the sum is equal to 1.

a. 0

b.

c. ½

d. ¼

21) A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is white?

a. 3/20

b. 7/20

c. 1/2

d. 17/20

e. 13/20

The next two questions refer to the following situation. The following list of Uniform

Resource Locators (URLs) contains some of the most visited sites on the World Wide

Web.

**URL Hits (millions)/day**

www.yahoo.com 12.5

www.msn.com 11.8

www.passport.com 6.3

www.hotmail.com 6.2

www.aol.com 5.1

www.iwon.com 2.9

www.excite.com 2.6

www.ebay.com 2.6

www.lycos.com 2.4

22) Based on the above data, what is the average and standard deviation, respectively?

a. 3.54, 3.60

b. 4.05, 3.60

c. 5.54, 3.79

d. 3.54, 3.79

e. 4.05, 10.1

23) Based on a graph of the above data, what is the shape?

a. Symmetric

b. Symmetric

c. Left-skewed

d. Right-skewed

e. Left-skewed

The distribution of the salaries of 100 employees at a small consulting firm is displayed in the following histogram. Suppose 95% of the data falls between 33 and 77.

24) Based on the empirical rule, what is the standard deviation of this sample of data?

a. 121

b. 22

c. 11

d. 5.5

e. 44

Consider the survey question “How much time does the chief executive officer spend at work?”

25) What type of data would this question collect?

a. Numerical, interval

b. Binomial

c. Categorical

d. Normal

e. Numerical, continuous

The manager of a small restaurant wishes to determine how long the average customer had to wait to be served during the lunch hour. At the lunch hour on a particular typical day, 10 customers experienced the following waiting times (in minutes):

7.5, 10.6, 10.2, 7.5, 5.3, 5.1, 10.0, 8.7, 4.0, 9.6

26) What is the shape of this data?

a. Right skewed

b. Binomial

c. Approximately symmetric

d. Left skewed

e. Normal

The following random sample of annual salaries was recorded. Units are in thousands of dollars.

50, 52, 48, 46, 32, 51, 47, 20, 53, 49

27) What are values of the average and median, respectively?

a. 48.5, 51

b. 44.8, 44.8

c. 48.5, 46

d. 44.8, 36.5

e. 44.8, 48.5

28) Stem-and-Leaf Display

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12 | 0

13 | 1 3 7 7

14 | 2 4 5

15 |

16 | 9 9

17 | 0 9

18 | 4

19 | 1 4

20 | 7

What is the shape of the data?

a. Normal

b. Left-skewed

c. Right-skewed

d. Approximately symmetric

e. Uniform

- 7 years ago