Download Test#3 - M. Ghamsary, Ph.D.

Math227
Test#3
Fall2007
Name:
---------------------------------------------------------------------------------------------------------------1A_Given that z is the standard normal variable (with mean 0 and standard deviation 1), find (15points)
a. P(1.23 ≤ z ≤ 2.35)
b. P(-1.28 ≤ z ≤ 1.39)
c. P12
1B_Given that x is normal variable with mean μ = 1000 and standard σ = 100, find
b. P(800<x ≤ 1000)
b. P(x >1250)
2.
The LDL value for population of certain city is approximately normal with a mean of 55mg/100ml and a standard
deviation of 10mg/100ml. If we randomly select a subject from this population, find the probability that the
individual will have a LDL level
(12points)
a. between 40 and 60
b. between 35 and 75
c. above 62
3.
d. below 40
The Customer Service Center in a large New York department store has determined that the amount of time spent
with a customer about a complaint is normally distributed with a mean of 10 minutes and a standard deviation of 2
minutes. What is the probability that for a randomly chosen customer with a complaint the amount of time spent
resolving the complaint will be
a.
Less than 14 minutes?
b.
More than 6 minutes?
c.
Between 8 and 12 minutes?
(12points)
1
3.
A simple random sample of size 20 is drawn from a normal population that is with 
Construct the 90% confidence interval about the population mean. (10points)
 8 and the sample mean of 75.
4.
A simple random sample of size 21 is drawn from a population that is known to be normally distributed. The sample
mean, x =100 and the standard deviation, s =15. Construct the 98% confidence interval about the population standard
deviation. (10points)
5.
The following data represent the age of a random sample of 12 from a large university. Assume that the scores for
each gender are normally distributed with no outliers
25
36
21
25
20
28
40
18
16
22
26
26
Construct the 95% confidence interval about the population mean (10points)
2
6.
Dr. Ghamsary wants to take a survey of families who own at least one gun. He wants to be 97% sure that the true
proportion of families who own at least one gun is no more that 2% or the true proportion. How large the sample
should be taken? (10 points)
6.
a.
If he has some idea of the past research about the estimate of this proportion and that is about 25%..
b.
If he has no prior knowledge of the proportion?
A health care professional wishes to estimate the birth weight of infants. How large a sample must she select if she
desires to be 90% confident that the true mean is within 6 ounces of the sample mean? The standard deviation of the
birth weights is known to be 8 ounces?
(10 points)
7.
A survey found that out of 300 workers, 240 said they were interrupted three or more times an hour by phone
messages, faxes, etc. Find the 92% confidence interval of the population proportion of workers who are interrupted
three or more times per hour. (10 points)
3