Math 200 Review for Exam 2
1. Using the binomial table find the probabilities of for a binomial random variable with n  15 and p  0.6 .
a. P( x  6)
d. P( x  4)
b. P( x  8)
e. P(4  x  6)
c. P(3  x  7)
f. P(3  x  9)
2. Twenty percent of the tires manufactured by a company are snow tires. Suppose 15 tires made by this
company are randomly selected. Find the probability that
a. 4 snow tires
c. at least 3 snow tires
b. at most 4 snow tires
d. at least 2 but no more than 4 are snow tires.
3. Find the mean and standard deviation of the number of defective universal joints in a sample of 500
manufactured by a machine that produces 2 percent defectives. What is the mean and standard deviation of
the non defective universal joints in a sample of 500 produced by the same machine?
4. Find the following probabilities for the standard normal distribution
a. P( z  2.37)
c. P( z  2.32)
b. P( z  1.32)
d. P(2.12  z  1.67)
5. Find the 80th, 90th, and 99th percentiles for the standard normal distribution.
6. Find the z-value for which the area :
a. to the left of z is 0.9881
d. to the right of z is 0.9989
b. to the right of z is 0.0250
e. between z and  z is 0.95
c. to the left of z is 0.0239
f. between z and  z is 0.7814
7. Suppose that the test scores for a college entrance exam are normally distributed with mean 405 and
standard deviation 100.
(a) What is percent score above 400?, below 300?, between 423 and 563?
(b) The upper 10% receive scholarships. What score must one get to receive a scholarship?
8. A consumer airline has found that the time required for a flight between two cities has approximately a
normal distribution with mean of 54.8 minutes and a standard deviation of 1.2 minutes.
a. Find the probability that a flight will take more than 56.6 minutes, between 50 and 60 minutes.
b. Find the 95th percentile of the flight time.
9. Explain the term sampling distribution.
10. A sample of size 3 is drawn from 2,4,5(with replacement).
a. List all possible samples
b. Calculate the sample mean for each sample.
c. Find the sampling distribution of the sample mean.
d. Find the sampling distribution of the sample median.
11. A population has a mean 500 and standard deviation 100. A sample of size 400 is randomly selected from
the population. Describe the sampling distribution of the sample mean.
12. An insurance company’s records show that the mean payout for all automobile claims is $1800 and the
standard deviation is $400. Suppose 90 claims are filed in one week. What is the probability they average
more than 1900? Between 1750 and 1850?
13. It is believed that 30% of all adults are overweight. How larger sample is necessary to estimate the true
proportion of adults who are overweight with a 95% confidence interval so that the margin of error of the
estimate is no greater than .03?
14. A poll of 2000 American adults showed that 1440 thought chemical dumps are among the most serious
health threats. Estimate with a 98% confidence interval the proportion of population who thinks the
chemical dumps are the most serious health threats. Interpret your answer.
15. To study the birth weight of infants whose mothers smoke, a physician records the weights of 100 newborns
whose mothers smoke. The sample mean found to be 6.1 pounds. If the population standard deviation is 2.1
pounds, construct and interpret a 98% confidence interval for the true mean birth weight of children of
Math 200 Exam2 Review
smoking mothers. What sample size is required so that the margin of error in determining the birth weight is
only .1 pounds?
16. The 28 surface water salinity measurements were taken in Whitewater bay yielded a sample mean of 49.54
with a standard deviation of 9.27. Construct the 98% confidence interval for the true mean salinity level.
Interpret your answer.
17. Using a t -distribution with given degrees freedom find the following:
a. df  15 , P(t  2.602)
f. df  19 , P(1.328  t  2.539)
b. df  22 , P(t  30505)
g. df  15 find t * so that
c. df  12 , P(t  3.055)
P (t *  t  t * )  .98
d. df  9 , P(t  1.383)
e. df  25 , P(1.316  t  2.787)
18. A sample of 32 commuters were asked how many miles they travel to work each day. Here are the data.
2.4 4.6 3.1 0.2 3.8 4.2 5.7 7.8 6.4 5.9
3.8 6.4 5.8 3.9 0.1 4.6 3.6 2.7 0.1 5.2 6.7
7.8 3.4 4.9 5.8 4.7 3.1 4.7 2.8 3.9 0.3 5.5
Construct the 95% confidence interval for the median miles traveled.