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Final
92. 01. 16
1. (20%)
A population has a standard deviation of 16.
(a) As the sample size n  100 , what is the probability that a sample
mean will be within  2 of the population mean (the sampling
error  2 )?
(b) Suppose the probability that a sample mean will be within  2 of
the population mean is 0.9. What is the sample size n?
2. (20%)
Assume the population proportion for the people skipping the breakfast is
25% and the sample proportion based on a sample of 300 data is
obtained.
(a) What is the probability that a sample proportion will be within
 0.05 of the population proprotion (the sampling error  0.05 )?
(b) What is the probability that a sample proportion will be between 22%
and 27%?
3. (20%)
Suppose we have a population of 40 elements
148 148 149 149 153 154 155 155 156 156
157 157 158 158 158 158 158 159 159 160
160 160 161 162 162 162 163 163 163 163
164 164 164 164 165 165 165 165 165 166
Suppose the first row of the table of random number is
63271 59986 71744 51102 15141 80714 58683 93108 13554 79945
Please use simple random sampling to obtain
(a) a sample of 5 elements.
(b) Construct a 90% confidence interval for the population mean.
4. (30%)
(a) Suppose the number of cars that arrive at a restaurant is described by a
Poisson distribution with a mean of 20 cars/per hour. What is the
probability that the time between the arrival is between 15 minutes and 45
minutes?
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(b) Let X be a continuous random variable with probability density
function
1 x
, c  x 1
2
.
 0, otherwise
f ( x) 
Find c and E  X  .
(c) You are applying for graduate school at University T. In the past
42% of the applicants to this university have been accepted. It is also
known that 70% of those students who have been accepted have had
entrance exam score in excess of 150 while 40% of the students who
were not accepted had extrance exam score in excess of 150. You take the
entrance exam and score 170. What is the probability that you will be
accepted into graduate school of University T?
5. (20%)
A random sample of 121 checking accounts at a bank showed an average
daily balance of $280. The standard deviation is known to be $60.
(a) Construct a 95% confidence interval for the average daily balance at
the bank.
(b) With 95% confidence, how many more checking accounts need to be
included in the sample to provide a confidence interval with length 10?
6. (10%)
The following observations are given for two variables
X
Y
2
5
12
8
3
18
6
20
11
22
19
30
18
10
9
7
(a) For the observations for variable X, compute the coefficient of
variation
(b) Compute the sample correlation coefficient for the two variables.
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