Solutions to the STA 210 Review Questions for Exam #3
This review does not cover all of the material on the exam. Questions on the exam will
come from material covered in the three sections of notes (III. A., III. B. and III. C.).
1) A box contains three poker chips (one red, one white, one blue) and two are drawn.
a. How many possible outcomes are there when the chips are drawn with
replacement?
33  9
b. Give the sample space when the chips are drawn with replacement.
red  R
white  W
blue  B
RR, RW , RB,WR,WW ,WB, BR, BW , BB
c. How many possible outcome are there if the chips are drawn without
replacement?
3 2  6
d. Give the sample space when the chips are drawn without replacement.
RW , RB,WR,WB, BR, BW 
2) A box contains four red and three blue poker chips. What is the probability when
three are selected randomly that all three will be red if we select each chip
a. with replacement?
 
3
4 4 4  4
 64
 0.187
7 7 7
7
343
b. without replacement?
4  3  2  24
 0.114
7 6 5
210
3) A survey of students at BCTC revealed the following employment breakdown:
Full-time
Part-time
Unemployed
TOTAL
75
75
50
200
Male
125
75
100
300
Female
200
150
150
500
TOTAL
A = {selected student is female}; B = {selected student works full time}
a. Find P A .
300
500
 0.6
b. Find PB  .
200
500
 0.4
c. Find P A and B  .
125
500
 0.25
d. Find P A or B  .
375
500
 0.75 or P A  PB  P A and B  0.6  0.4  0.25  0.75
e. Find PA .
200
500
 0.4 or 1  P A  1  0.6  0.4
f. Find P A | B  .
125
200
 0.625 or
P A and B  0.25

 0.625
P B 
0.4
g. Are events A and B mutually exclusive?
No, P A and B   0
h. Are events A and B independent?
No, P A  P A | B 
4) The number of calls x to arrive at a switchboard during any 1-minute period is a
random variable and has the following probability distribution:
0
0.1
x
P(x)
1
0.1
2
0.4
3
0.2
4
0.2
a. Find the mean.
   x  Px   2.3
b. Find the variance.
 2   x 2  Px    2  6.7  2.32  1.41
c. Find the standard deviation.
  1.41  1.187
P x 
0.1
0.1
0.4
0.2
0.2
x
0
1
2
3
4
x  P x 
0
0.1
0.8
0.6
0.8
 x  Px  2.3
x2
0
1
4
9
16
x 2  P x 
0
0.1
1.6
1.8
3.2
2
 x  Px  6.7
5) Computers are shut down for certain periods of time for routine maintenance,
installation of new hardware, and so on. The downtimes for a particular computer are
normally distributed with a mean of 1.5 hours and a standard deviation of 0.4 hours.
a. Based on the empirical rule, 68% of the downtimes will be within what
interval?
   ,    
1.5  0.4 , 1.5  0.4
1.1 , 1.9
b. What is the z-score for the observation of 0.75 hours?
Z
x


0.75  1.5
 1.875
0.4
c. What is the probability that a downtime will be less than 1 hour?
Z
x


1  1.5
 1.3
0.4
Px  1
 PZ  1.3
 0.0968
d. What is the probability that a downtime will exceed 2.1 hours?
Z
x


2.1  1.5
 1.5
0.4
P  x  2.1
 P  Z  1 .5 
 1  0.9332
 0.0668
e. What is the probability that a downtime will be between 0.5 and 2.5 hours?
x
0.5  1.5
 2.5

0.4
x   2.5  1.5
Z

 2.5

0.4
Z

P0.5  x  2.5
 P 2.5  Z  2.5
 0.9938  0.0062
 0.9876
f. Find the x value for which 90% of the downtimes will be less.
x    Z
 1.5  0.41.3
 2.02