Download MAT201 Sample Test 1 (Spring 2017)

MAT201 Sample Test 1 (Spring 2017)
Instructor: Myung Soon Song
Printed Last Name _______________________
Printed First Name __________________
Section ____________________________
You MUST show your work to get full credit for work out questions.
Use the following to answer Questions 1–2
Scores on a university exam are Normally distributed with a mean of 70 and a standard deviation of 10.
The professor teaching the class declares that a student will receive a “F” if his or her score is below
50.
1. Using the 68-95-99.7 rule, what percent of students will receive “F”?
2.5%
2. Using the 68-95-99.7 rule, what percent of students will score between 60 and 90?
81.5%
3. Using the standard Normal distribution tables, the area under the standard Normal curve corresponding
to –1.0 < Z < 1.0 is:
a. 0.3085.
* b. 0.6828.
c. 0.5328.
d. 0.2815.
4. A density curve has which of the following properties?
a. It is always negative.
b. It has the area of 0.5 under the curve over whole range of x.
c. It is always symmetric.
* d. None of the above
Use the following to answer Questions 5 and 6. (Use Table A)
A company produces packets of soap powder labeled “Giant Size 32 Ounces.” The actual weight of soap
powder in such a box has a Normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz.
To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it
weighs less than 32 oz. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight.
1
5. What proportion of boxes is underweight (i.e., weigh less than 32 oz)?
0.0764
6. How heavy does a box have to be for it to be labeled overweight?
a. 31.60 oz
b. 31.85 oz
* c. 34.15 oz
d. 34.40 oz
Use the following to answer Questions 7 and 8. (Use Table A)
The duration (in days) of human pregnancies follows approximately the N(266,16) distribution.
7. How many days would a human pregnancy need to last to be among the top 10% of all durations?
a. 239.68 days
b. 245.52 days
* c. 286.48 days
d. 292.32 days
8. What proportion of pregnancy durations are more than 270 days?
0.4013
9. The time taken for a computer link to be made between the terminal in an executive’s office and the
computer at a remote factory site has a Normal distribution with a mean of 15 seconds and a standard
deviation of 3 seconds. On 90% of the occasions, the computer link is made in less than __________ .
18.84 seconds.
Use the following to answer Questions 10–13.
A violin student records the number of hours she spends practicing during each of nine consecutive
weeks.
6.2
5.0
4.3
7.4
5.8
7.2
8.4
1.2
6.3
10. What is the mean number of hours spent practicing per week during this period?
5.76 hours
11. What is the median number of hours spent practicing per week during this period?
6.20 hours
12. What is the interquartile range (IQR) for this data?
2.65 hours
13. Considering the smallest data value (1.2) and using the 1.5 × IQR rule, we would
a. classify the value 1.2 as an outlier, because it is more than 1.5 × IQR’s below the first quartile.
* b. not classify the value 1.2 as an outlier because it is not more than 1.5 × IQR’s below the first
quartile.
c. classify the value 1.2 as an outlier because it is more than 1.5 × IQR’s below the median.
d. classify the value 1.2 as an outlier because it is more than 1.5 × IQR’s below the mean.
14. Calculate the sample variance of the data set {2, 4, 9, 11, 13, 15} by using the table method you
learned in class.
𝑠 2 = 26
Use the following to answer Questions 15–16.
The exam scores (out of 100 points) for all students taking an introductory Statistics course are used to
construct the following boxplot.
15. Based on this boxplot, which of the following statements is true?
* a. The distribution of scores is fairly symmetric.
b. About half the students scored below 52.
c. Nobody scored above 90.
d. All of the above
16. If 5 points were added to each score, then standard deviation of the new scores would
a. be increased by 5.
b. be increased by 25.
c. be decreased by 5.
* d. remain unchanged.
17. What plots can you use for one numerical variable? Write more than one.
Histogram, stemplot
18. Employees at a large company are surveyed about the status of their health insurance status.
Employees are coded as “1” if health insurance is obtained through the company’s benefit program, “2” if
it obtains health insurance from another source (e.g., through a spouse’s employment benefit program), or
“0” if the employee does not have health insurance. The variable class standing is
a. numerical.
* b. categorical.
c. quantitative.
d. All of the above
19. A company has three divisions and three conference rooms for meetings. To keep track of the use of
their facilities, for each meeting held in the company, the division holding the meeting is recorded, the
room for the meeting is recorded, and the length of time of the meeting is recorded. Which of the
variables is quantitative?
a. the division holding the meeting
b. the conference room for the meeting
* c. the length of time for the meeting
d. All of the above
Use the following to answer Questions 20 and 21.
A sample of 40 employees from the local Honda plant was obtained and the length of time (in months)
worked was recorded for each employee. A stemplot of these data follows. In the stemplot, 5|2
represents 52 months.
5
6
7
8
9
2233457899
0002344456778889
3455667778899
8
20. What would be a better way to represent this data set?
a. Display the data in a time plot.
* b. Split the stems.
c. Use a pie chart.
d. Use a histogram with class width equal to 20.
21. The percentage of employees in the sample that have worked at the plant for more than 7 years is
* a. 2.5%.
b. 25%.
c. 15%.
d. 5%.