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
B
123
249
280
C
24
61
77
D
11
36
45

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)=


P(B)=


P(C)=



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

  1. Compute the following:

P(1976)=


P(1980)=



P(1986)=




Explain the meaning of these numbers (1 point).







  1. Compute following:

P(1976|A)


P(C|1980)


Explain what each means (1 point):





  1. Compute P(A or B).


Are these events mutually exclusive? (1 point)


  1. Compute the following:

P(B and 1976)



P(D and 1986)



  1. Compute P(B or 1976).

Are these events mutually exclusive? (1 point)


2.

  1. 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)

     

     

     

     

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

     
3.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.













  1. Calculate the expected value.








  1. Calculate the standard deviation.






  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.








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