STAT 200 Spring 2019 Midterm Examination
1
Dr. K. Thengumthara Name:
STAT 200 Spring 2019 Midterm Examination
This is an open-book exam. You may refer to your text and other course materials for the current
course as you work on the exam, and you may use a calculator. You must complete the exam
individually. Neither collaboration nor consultation with others is allowed. It is a violation of the
UMUC Academic Dishonesty and Plagiarism policy to use unauthorized materials or work from
others.
Download the answer sheet. Answer all 20 questions. Submit ONLY the answer sheet as a single
pdf document by EST 11:59PM on Sunday March 31, 2019. Make sure your answers are as
complete as possible. Show all of your supporting work and reasoning. Answers that come
straight from calculators, programs or software packages without any explanation will not be
accepted. If you need to use technology (for example, Excel, online or hand- held calculators,
statistical packages) to aid in your calculation, you must cite the sources and explain how you get
the results.
Questions: 1-10. 2points each. Select the right answer.
1. Stratified sampling___
a. Can be more representative than simple randomized sampling
b. Can be used if the population has a number of distinct groups
c. Is done by randomly sampling from subgroups in a way that is proportional to
their size in the population
d. All of the above
2.Which of the following is a qualitative variable?
a. Weight in pounds
b. Number of days of precipitation
c. Race
d. Average daily high temperature
3. A normal distribution has a mean of 20 and a standard deviation of 4. Find the Z
scores of 28.
a. 1
b. -1
c. 2
d. -2
2
4. A Z-score represents the number of standard deviations above or below the
mean.
a. True
b. false
5. Which of the following is a quantitative variable?
a. Gender
b. Religion
c. Ethnicity
d. Average daily temperature
6. The area under the curve of a probability distribution is _____
a. 0
b. 100
c. 0.68
d. 1
7. Amount of money is measured on what type of scale?
a. Nominal
b. Ordinal
c. Interval
d. Ratio
8. The following distribution has:
a. A positive skew
b. A left skew
c. No skew
9. Which of the following are measures of variability?
a. mean
b. median
c. mode
d. standard deviation
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10. A sample of only those students seated in the front row of class would be an
unbiased sample.
a. True
b. False
Questions 11-20: 8 points each. Show all necessary work.
11. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new AIDS antibody drug is
currently under study. It is given to patients once the AIDS symptoms have
revealed themselves. Of interest is the average (mean) length of time in months
patients live once starting the treatment. The following data (in months) was
collected.
3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21;
22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34
Complete the tables using the data provided:
Survival
Length (in
months)
Frequency Relative
Frequency
Cumulative Relative
Frequency
0.5–6.5
6.5–12.5
12.5–18.5
18.5–24.5
24.5–30.5
30.5–36.5
12. A person’s metabolic rate is the rate at which the body consumes energy.
Metabolic range is important in the studies of weight gain, dieting and exercise.
Here are the metabolic rates of 7 men who took part in a study of dieting. The units
are calories per 24 hours.
1792, 1666, 1362, 1614, 1460, 1867, 1439
4
Find the variance and standard deviation of the metabolic rates. (Give the formula
and show all necessary work. Round the answer to two decimal places.
Metabolic rate, x x- mean (x- mean)2
13. A refrigerator contains 7 apples, 4 oranges, 9 bananas, 3 pears, 8 peaches, 10
plums, and 4 mangos. (8 points)
(i) Imagine you stick your hand in this refrigerator and pull out a piece of fruit at
random. What is the probability that you will pull out a pear?
(ii) What is the probability that you stick your hand in the refrigerator one time and
pull out a mango or an orange?
(iii) The probability that the piece of fruit you pull out is not peach.
14. In how many different ways can a student select to answer five questions from
a test that has seven questions, if the order of the selection is not important?
15. An experiment is rolling a fair die and then flipping a fair coin.
(i) State the sample space.
(ii) Find the probability of getting a head.
(iii) Find the probability of getting a 6 or a head.
(iv) Find the probability of getting a 3 and a tail.
16. Suppose a random variable, x, arises from a binomial experiment. If n = 8, and
p = 0.70, find the following probabilities using technology. Round he answer to 3
decimal places.
(i) P(x=2)
5
(ii) P(x< 3)
(iii) P(x≥ 5)
17. According to an article in the American Heart Association’s publication
Circulation, 24% of patients who had been hospitalized for an acute myocardial
infarction did not fill their cardiac medication by the seventh day of being
discharged (Ho, Bryson & Rumsfeld, 2009). Suppose there are twelve people who
have been hospitalized for an acute myocardial infarction.
Find the following probability
(i) All filled their cardiac medication.
(ii) None filled their cardiac medication.
(iii) At most two did not fill their cardiac medication.
(iv) At least five did not fill their cardiac medication.
18. A retailer offers an extended warranty on a new television.The cost of the warranty is $116.The warranty stipulates that the retailer will replace the television if
any failure occurs during the warranty period. They estimate that the probability of
product failure during the warranty period is 3.4%, and that the cost of replacing the
television is $2160. Find the expected value, for the company, of a warranty. Round
your answer to two decimal places.
19. Assume the speed of vehicles along a stretch of I-10 has an approximately
normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
(i) The current speed limit is 65 mph. What is the proportion of vehicles less than
or equal to the speed limit?
(ii) What proportion of the vehicles would be going more than 80 mph?
20. The mean yearly rainfall in Sydney, Australia, is about 137 mm and the
standard deviation is about 69 mm ("Annual maximums of," 2013). Assume
rainfall is normally distributed.
(i) Find the probability that the yearly rainfall is more than 240 mm.
(ii) Find the probability that the yearly rainfall is between 140 and 250 mm.
(iii) If a year has a rainfall less than 100mm, does that mean it is an unusually dry
year? Why or why not?
(iv) What rainfall amount are 90% of all yearly rainfalls more than?