Solutions only, no work needed:

1. The following table gives the cumulative frequency distribution of the commuting time (in minutes) from home to work for a sample of 400 persons selected from a city.

Time (minutes)

f

0 to less than 10

64

0 to less than 20

159

0 to less than 30

219

0 to less than 40

278

0 to less than 50

355

0 to less than 60

400

A. The sample size is:

B. The percentage of persons who commute for less than 30 minutes, rounded to two decimal places, is:

C. The cumulative relative frequency of the fourth class, rounded to four decimal places, is:

D. The percentage of persons who commute for 40 or more minutes, rounded to two decimal places, is:

E. The percentage of persons who commute for less than 50 minutes, rounded to two decimal places, is:

F. The number of persons who commute for 20 or more minutes is:

2. The temperatures (in degrees Fahrenheit) observed during seven days of summer in Los Angeles are:

789968911007585

A. The range of these temperatures is:

B. The variance of these temperatures, rounded to three decimals, is:

C. The standard deviation, rounded to three decimals, of these temperatures is:

3. The following table gives the two-way classification of 500 students based on sex and whether or not they suffer from math anxiety.

Suffer From Math Anxiety

Sex

Yes

No

Male

170

70

Female

165

95

A. If you randomly select one student from these 500 students, the probability that this selected student is a female is:

(round your answer to three decimal places, so 0.0857 would be 0.086)

B. If you randomly select one student from these 500 students, the probability that this selected student suffers from math anxiety is:

(round your answer to three decimal places, so 0.0857 would be 0.086)

C. If you randomly select one student from these 500 students, the probability that this selected student suffers from math anxiety, given that he is a male is:

(round your answer to three decimal places, so 0.0857 would be 0.086)

D. If you randomly select one student from these 500 students, the probability that this selected student is a female, given that she does not suffer from math anxiety is:

(round your answer to three decimal places, so 0.0857 would be 0.086)

E. Which of the following pairs of events are mutually exclusive?

No and yes

Female and no

Male and yes

Female and male

Female and yes

Male and no

F. Are the events "Has math anxiety" and "Person is female" independent or dependent? Detail the calculations you performed to determine this.

Independent or dependent

4. The following table lists the probability distribution of a discrete random variable x:

x 2 3 4 5 6 7 8

------------------------------------------------------------------------

P(x) 0.15 0.33 0.21 0.13 0.10 0.06 0.02

A. The mean of the random variable x is:

B. The standard deviation of the random variable x, rounded to three decimal places, is: