Download 1) Determine the probability distribution`s missing value

Cuyamaca College
Math 160+060
Name:__________________
Instructor: Dan Curtis
Practice Exam 3
1) Determine the probability distribution’s missing value.
x
P(x)
0
0.2
1
0.2
2
?
3
0.3
4
0.1
2) The random variable x represents the number of credit cards that adults have along
with the corresponding probabilities. Find the mean of the probability distribution.
x
0
1
2
3
4
P(x)
0.1
0.1
0.3
0.3
0.2
3) Find the z-score that has 45% of the distribution’s area to its right.
4) IQ test scores are normally distributed with a mean of 100 and a standard deviation of
15. An individual’s IQ score is found to be 125. Find the z-score that corresponds to this
value.
5) A particular brand of batteries has a mean lifespan of 570 hours, with a standard
deviation of 80 hours. If 64 batteries are randomly selected, find the probability that they
have a mean lifespan between 565 hours and 575 hours.
6) Which score is better: a score of 38 on a test with a mean of 30 and a standard
deviation of 5 and a score of 144 on a test with a mean of 130 and a standard deviation of
15.
A) You cannot determine which score is better from the given information.
B) A score of 38 with a mean of 30 and a standard deviation of 5 is better.
C) A score of 144 with a mean of 130 and a standard deviation of 15 is better.
D) The two scores are statistically the same.
7) Assume that the weight of adult giant pandas are normally distributed with  = 250
pounds and  = 15. Would it be unusual to find an adult giant panda that weighed more
than 300 pounds? Support your answer.
8) Use the standard normal distribution to find P(-1.0 < z < 2.0).
9) The average number of pounds of sugar a person consumes each year is 156 with a
standard deviation of 22 pounds (Source: American Dietetic Association). If a sample of
36 individuals is randomly selected, find the probability that the mean of the sample will
be greater than 160 pounds.
10) The lengths of pregnancies of humans are normally distributed with a mean of 268
days and a standard deviation of 15 days. What percentage of babies are born more than
two weeks early?
11) Assume that the salaries of elementary school teachers in the United States are
normally distributed with a mean of $35,000 and a standard deviation of $4000. What is
the cutoff salary for teachers in the bottom 20%?
12) Given the same sample statistics, which level of confidence will produce the
narrowest confidence interval?
A) 95% B) 90% C) 85% D) 80%
13) Find the critical value zc that corresponds to an 80% confidence level.
14) For each claim, determine the null and alternate hypotheses, and determine whether
each claim is a left-tailed, right-tailed or two-tailed test.
(a) A battery manufacturer claims that the mean life of its batteries is more than
1000 hours.
(b) A cigarette maker claims that no more than 20% of Americans smoke.
(c) A study claims that the mean survival time for certain cancer patients treated
immediately with chemotherapy and radiation is 24 months.
15) A computer repairer believes that the mean repair cost for damaged computers is
more than $95. To test this claim, you determine the repair cost for 12 randomly selected
computers and find that the mean repair cost is $100, with a standard deviation of $12.50.
At   0.05 , do you have enough evidence to support the repairer’s claim?
16) In your work for a national health organization, you are asked to monitor the sodium
in a certain brand of cereal. You find that a random sample of 100 cereal servings has a
mean sodium content of 232 milligrams with a standard deviation of 10 milligrams.
At   0.04 , is there enough evidence to support the claim that the mean sodium content
per serving of cereal is less than 234 milligrams?
17) A survey of 280 homeless persons showed that 63 were veterans. Construct a 90%
confidence interval for the proportion of homeless persons who are veterans.
18) A random sample of 16 fluorescent light bulbs has a mean life of 645 hours with a
standard deviation of 31 hours. Assume the population has a normal distribution.
Construct a 95% confidence interval for the population mean, μ.
Practice Exam Solutions
1) 0.2
2) µ = 2.4,   1.2
3) .126
4) 1.67
5) .383
6) B
7) P(x>300)=0.000429, Very unusual
8) .819
9) .138
10) .175
11) $31633.52
12) D
13) invNorm(0.10) = -1.28, so zc  1.28
14) (a) Claim: μ > 1000
H0 : μ _ 1000
Ha : μ > 1000
Right-tail test
(b) Claim: p _ .20
H0 : p _ .20
Ha : p > .20
Right-tail test
(c) Claim: μ = 24
H0 : μ = 24
Ha : μ 6= 24
Two-tail test
15) Claim:   95
Opposite:   95
H 0 :   95
H a :   95
x  100
  12.50
n  12
P  .083  
Fail to reject H 0
There is not enough evidence to support the claim.
16) Claim:   234
Opposite:   234
H 0 :   234
H a :   234
x  232
  10
n  100
P  .023  
Reject H 0
There is enough evidence to support the claim.
17) Confidence Interval:
63
pˆ 
 .225
280
qˆ  .775
zc  1.645
(.225)(.775)
 .041
280
.184  p  .266
18) Confidence Interval:
zc  1.96
E  1.645
 31 
E  1.96 
  15.19
 16 
629.81    660.19