Question

The distribution of Master’s degrees conferred by a university is listed in the table.

Major	Frequency
Mathematics	216
English	207
Engineering	86
Business	176
Education	267

What is the probability that a randomly selected student graduating with a Master’s degree has a major of Education or a major of Engineering?

A. 0.371 B. 0.720 C. 0.390 D. 0.280

2.

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam.

Hours, ?	3	5	2	8	2	4	4	5	6	3
Scores, ?	65	80	60	88	66	78	85	90	90	71

A). Calculate the correlation coefficient.

B). Find the equation of the regression line.

C). Use the regression equation to predict the test score of a student who studied for 5.5 hours.

3. Find the ?-score for which 70% of the distribution’s area lies to its right.

A. -0.52 B. -0.98 C. -0.48 D. -0.81

4. A group of 49 randomly selected students has a mean age of 22.4 years. Assume the population standard deviation is 3.8. Construct a 98% confidence interval for the population mean.

A. (20.3, 24.5) B. (18.8, 26.3) C. (21.1, 23.7) D. (19.8, 25.1)

5.Use fundamental counting principle to determine how many license plates can be made consisting of 3 different letters followed by 2 different digits.

A. 1,757,600 B. 175,760 C. 100,000 D. 1,404,000

6. A group of students were asked if they carry a credit card. The responses are listed in the table.

Class	Credit Card	No Credit Card	Total
Freshmen	40	20	60
Sophomore	25	15	40
Total	65	35	100

If a student is selected at random, find the probability that he/she owns a credit card given that the student is a freshman.

A. 0.400 B. 0.615 C. 0.667 D. 0.333

7. Use the standard normal distribution to find ?(−2.50 < ? < 1.50).

A. 0.8822 B. 0.5496 C. 0.6167 D. 0.9270

8.

The number of home runs that Barry Bond hit in the first 18 years of his major league career are listed.

16 25 24 19 33 25 37 41 37

25 42 40 37 34 49 73 46 45

A). Find the mean.

B). Find the median.

C). Find the mode.

Answer 1

1.

Total frequency =216+...+267 =952

P(Education) =267/952 =0.2805

P(Engineering) =86/952 =0.0903

P(Education or Engineering) =0.2805 + 0.0903 =0.3708

Thus, the probability that a randomly selected student graduating with a Master’s degree has a major of Education or a major of Engineering =0.3708

2.

A)

The correlation coefficient, r =0.8465

B)

The regression equation is: = 5.0443X + 56.11392

C)

X =5.5 hours

=5.0443(5.5) + 56.11392 =83.85757

(can be rounded to 84)

3.

The ?-score for which 70% of the distribution’s area lies to its right is: Z = -0.52

Option A. is correct.

4.

Sample size, n =49

Sample mean, =22.4

Population standard deviation, =3.8

Since n > 30 (large sample) and population standard deviation is known, we shall use Z-score.

For 98% confidence level, for a two-tailed case, Z_crit =2.33

Standard Error, SE = =0.543

Margin of Error, MoE =Z_crit*SE =2.33*0.543 =1.265

98% confidence interval for the population mean, =22.4 1.265 =(21.1, 23.7)

Option C. is correct.

5.

Number of license plates that can be made consisting of 3 different letters =P(n, r) =P(26, 3) =15600

(since there are n =26 letters available: A - Z).

Number of license plates that can be made consisting of 2 different digits =P(n, r) =P(10, 2) =90

(since there are n =10 digits available: 0 - 9).

Number of license plates that can be made consisting of 3 different letters followed by 2 different digits =15600*90 =1404000

6.

The probability that he/she owns a credit card given that the student is a freshman =40/60 =0.667

Option C. is correct.

7.

?(−2.50 < ? < 1.50) =0.9270

Option D. is correct.

8.

A) Mean = =648/18 =36

B) Median =middle most value (or the average of two middle most values) after arranging the data in an ascending order =37

C) Mode =most frequently occured value (or values) =25, 37