Key 2 - Practice Exam No. 2

1.

The following is based on information from the Statistical Abstract of the U.S., 1992. In this table, the columns are years in which students graduated from college with a bachelor's degree. The rows are high school grade averages for these students. In 1976, therefore, a random sample of 577 new college graduates showed that 419 had a high school grade average of A, 123 had a high school grade average of B, and so on.

 

High School Grade Average

 

1976

 

1980

 

1986

 

 

A

419

593

607

1619

 

B

123

249

280

652

 

C

24

61

77

162

 

D

11

36

45

92

 

 

577

939

1009

2525

 


Suppose that a college graduate is selected at random from the pool of 1976, 1980, and 1986 graduates. Let us use the following notation for events:

1976 = event a student graduated from college in 1976

A = event a student had a high school grade average of A

(2 points each unless noted)

a) Compute the following :

P(A)= 1619/2525 = 64%

P(B)= 652/2525=26%

P(C)= 162/2525=6%

Explain the meaning of these numbers. Is a college graduate more likely to have had a higher grade average in high school? (1 point)

Yes. Higher percentage of graduates had A grade averages in high school.

 
  1. Compute the following:

P(1976)= 577/2525=23%

P(1980)=939/2525=37%

P(1986)=1009/2525=40%


Explain the meaning of these numbers (1 point).

Of the students sampled, the chances of selecting someone who graduated in 1976 is 23%. The probability of selecting someone who graduated in 1980 is 37% and the probability of selecting someone who graduated in 1986 is 40%

 
  1. Compute following:

P(1976|A) = 419/1619=26%

P(C|1980)=61/939=6%

Explain what each means (1 point):
Of all the students with A's in high school, 26% graduated in 1976.

Of all the students who graduated in 1980, 6% graduated with C's in high school.

 
  1. Compute P(A or B)=(1619+652)/2525=90%

Are these events mutually exclusive? (1 point)
Yes, you can not graduate with both A and B grades.

 
  1. Compute the following:

P(B and 1976) =123/2525=5%

P(D and 1986)=45/2525=2%

 
  1. Compute P(B or 1976)= 652/2525+577/2525-123/2525=43%.

Are these events mutually exclusive? (1 point)
No, can graduate from college in 1976 and have B grade in high school.

2.

A car dealership kept records of all daily sales for one year and the following distribution was tabulated. 

No. cars sold

0

1

2

3

4

5

 

 

 

 

Percent of total

.1

.1

.2

.2

.3

.1

 

 

 

 

What is the expected value of cars sold per day? (4 points)

 

 What is the standard deviation? (4 points)

 

0

1

2

3

4

5

 

 

0.1

0.1

0.2

0.2

0.3

0.1

Average

 

0

0.1

0.4

0.6

1.2

0.5

2.8

STD

0.784

0.324

0.128

0.008

0.432

0.484

2.16

1.469694

What are the chances three or more cars will be sold? (2 points)

P(3) + P(4) + P(5) = .2+.3+.1 = .6





 

A waiter at the Red Riding Restaurant has learned from long experience that the probagility that a lone diner will leave a tip is only 70%. During one lunch hour he serves six people who are dining by themselves. (3 points each)

  1. Make a graph of the binomial probability distribution. Note the page of any table look-ups.  (From Table)

 
  1. Calculate the expected value.

E(X)=np=6*.7=4.2





  1. Calculate the standard deviation.

Sigma = Square root (np(1-p) = 1.122



  1. If each diner leaves an average tip of $2, what is the probability that the waiter will earn more than $6 in tips that lunch hour.

$6 equals 3 diners (at $2 each) therefore looking for P(more than 3 diners)

P(4,5,6)=.32+.3+.12=.74