Chapter 8 Continuous Probability Models
Chapter 8 Practice
1. Suppose the commuting time from Georgetown to Washington varies uniformly from 20 to 45
min, depending on traffic and weather conditions. Construct a graph of this distribution and use
the graph to find
a) The probability that a trip takes less than 30 min
b) The probability that a trip takes more than 40 min
Probability Density Value 
1
 0.04
45  20
0.04
20
a) P (x  30)  0.04 10   0.40
45
b) P (x  40)  0.04 5   0.2
2. A cookie manufacturer is randomly testing the diameter size of his companies’ cookies. He
finds that the distribution of cookies is approximately normal with a mean diameter of 9.6 cm
and a standard deviation of 1.13 cm. A cookie is rejected if it is too big (in the top 10%). What
is the probability that
a) A randomly selected cookie has a diameter greater than 11 cm
b) A randomly selected cookie has a diameter between 8.8 and 10.3 cm
c) A cookie is rejected if it has a diameter of 11.8 cm
a) P (x  11)  0.1077
b) P (8.8  x  10.3)  0.4927
c) P (x  11.8)  0.0258
In the top 10%, therefore rejected.
3. Adrian’s average bowling score is 174, with a standard deviation of 35.
a) In what percent of games does Adrian score less than 200 points? At least 200 points?
b) The top 10% of bowlers in Adrian’s league get to play in an all-star game. If the league
average is 170, with a standard deviation of 11 points, what average score does Arian need to
have to obtain a spot in the all-star game?
a) P (x  199.5)  0.7642
b) Needs a score of 184.
P (x  199.5)  0.2358
4. The masses of statistics students are believed to be normally distributed. The masses (in
kilograms) of a random sample of 36 statistics students are
62
63
63
64
64
65
67
67
68
68
68
68
66
67
67
67
68
68
70
70
70
71
71
71
70
71
71
71
71
72
74
75
75
77
77
78
a) Determine the mean and standard deviation of these data.
b) What is the probability that the mass of a randomly selected statistics student will be at
least 70 kg?
c) Of 120 statistics students, how many would you expect to have a mass greater than 65 kg?
a) x  69.3
s  4.02
c) P (x  65)  0.8576
b) P (x  70)  0.4309
1000  0.8576  103 students
5. A multiple choice exam contains 50 questions and each question has 4 answers from which to
choose. If a student merely guesses at the answers, what is the probability that
a) The student will get 10 questions correct
b) The student will pass
a) np  12.5,
npq  3.06
P (9.5  x  10.5)  0.0930
b) P (x  24.5)  0.00004
6. A machine produces articles and an average of 2% of theses articles are defective. IN a batch
of 400 articles what is the probability that no more than 4 are defective.
np  8,
npq  2.8
P (X  4.5)  0.1035
7. The theoretical probability of winning at the dice games, craps, is 0.493. If you play 50 games
in Las Vegas, what is the probability that you will win more than you lose?
np  24.65,
npq  3.54
P (X  25.5)  0.4051
8. The fuel consumption for a new model of automobile is normally distributed with a mean of
30 km/L and a standard deviation of 3 km/L. Each week, the manufacturer asks 100 randomly
selected owners of this new model to keep track of their fuel consumption.
a) Find the mean and standard deviation of the means of these samples.
b) How likely is the manufacturer to find a sample mean of 29 km/L or less?
a) x  30 σx 
3
100
b) P(X ≤29) = 0.0004
9. A major soft drink company is interested in determining whether the company has made a
significant improvement in its market share after a year long advertising campaign. The
company has had a 24% share of the market historically. In a random sample of 500 customers,
there are 152 of its products. Test whether there is a statistically significant increase in its
market share at a significance level of 5%.
H0 : p  24%
H1 : p  24%
np  120
P(X > 151.5) = 0.0004
npq  9.55
Since P   152   accept H1
 There has been a significant increase in the market share.
10. In a manufacturing process it has been found that 99.5% of the products are defect-free. A
new process is introduced to improve the quality of the product. If in a batch of 3000, 2993
are defect free, has the new process significantly improved the quality of the product. Make a
hypothesis test at a significance level of 10%.
H0 : p  99.5%
H1 : p  99.5%
np  2985
npq  3.86
P(X > 2992.5) = 0.0004
Since P   2993   accept H1
 There has been a significant improvement to the quality.
11. A poll of 200 residents found that 73.0% support a new plan to revitalize a city’s waterfront.
Determine a 95% confidence interval for support for the revitalization plan.
p  z
2
0.73  1.96
pq
n
0.73  0.27 
200
 p  p  z
2
pq
n
 p  0.73  1.96
0.6685  p  0.7915
0.73  0.27 
200