STAT 200

Spring 2020

Midterm Exam

**Please answer all 10 big questions. The maximum score for each question is posted at the beginning of the question, and the maximum score for the Midterm Exam is 100 points. **

**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.**

**
IMPORTANT:
** You are requested to include a brief note at the beginning of your submitted quiz, confirming that your work is your own. The note should say, “I have completed this assignment myself, working independently and not consulting anyone.” Your submitted quiz will be accepted

**you have included this statement.**

only if

only if

**
Problem # 1 (6 points)
**Choose the best answer. Justify for full credit.

(a) UMUC Stat Club conducted a survey on STAT 200 study hours. The survey result showed that 54% of the respondents spent more than 20 hours each week on STAT 200. The value 54% is a

i (i) statistic

ii (ii) parameter

iii (iii) cannot be determined

(b) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is

i (i) interval

ii (ii) nominal

iii (iii) ordinal

iv (iv) ratio

(c) UMUC STAT Club wanted to estimate the study hours of STAT 200 students. Two STAT 200 sections were randomly selected and all students from these two sections were asked to fill out the questionnaire. This type of sampling is called:

i (i) cluster

ii (ii) convenience

iii (iii) systematic

iv (iv) stratified

Problem # 2 (6 points)

The Affordable Care Act created a market place for individuals to purchase health

care plans. In 2014, the premiums for a 27 year old for the bronze level health

insurance are given in **Table 1**

**Table 1: Data of Health Insurance Premiums
**

a) Create a frequency distribution, relative frequency distribution, and cumulative

frequency distribution using 5 classes.

b) Create a histogram and relative frequency histogram for the data in Table 1

Describe the shape and any findings you can from

the graph.

c) Create an ogive for the data in Table 1. Describe any findings you can from

the graph.

**
Problem # 3 (6 points)
**Eyeglassmatic manufactures eyeglasses for their retailers.

They test to see how many defective lenses they made the time period of January 1 to March 31. **Table 2
**gives the defect and the number of defects.

**Table 2: Number of Defective Lenses**

a.) Find the mean and median.

b.) Find the range.

c.) Find the variance and standard deviation.

Problem # 4 (10 points)

An experiment is rolling a fair die and then flipping a fair coin.

a.) State the sample space.

b.) Find the probability of getting a head. Make sure you state the event space.

c.) Find the probability of getting a 6. Make sure you state the event space.

d.) Find the probability of getting a 6 or a head.

e.) Find the probability of getting a 3 and a tail.

Problem # 5 (5 points)

You have a group of **twelve** people. You need to pick a president, treasurer, and

secretary from the twelve. How many different ways can you do this?

Problem # 6 (12 points)

Suppose a random variable, x, arises from a binomial experiment. If n = 22, and p

= 0.85, find the following probabilities using the binomial formula.

a.) Px 18

b.) Px 5

c.) Px 20

d.) Px ≤3

e.) Px ≥18

f.) Px ≥20

Problem # 7 (18 points)

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.

Suppose there are twelve people who have been hospitalized for an acute myocardial infarction.

a.) State the random variable.

b.) Argue that this is a binomial experiment

Find the probability that

c.) All filled their cardiac medication.

d.) Seven did not fill their cardiac medication.

e.) None filled their cardiac medication.

f.) At most two did not fill their cardiac medication.

g.) At least three did not fill their cardiac medication.

h.) At least ten did not fill their cardiac medication.

i.) Suppose of the next twelve patients discharged, ten did not fill their cardiac

medication, would this be unusual? What does this tell you?

Problem # 8 ( 14 points)

Eyeglassomatic manufactures eyeglasses for different retailers. In March 2010, they tested to see how many defective lenses they made, and there were 16.9% defective lenses due to scratches. Suppose Eyeglassomatic examined **twenty** eyeglasses.

a.) State the random variable.

b.) Write the probability distribution.

c.) Draw a histogram.

d.) Describe the shape of the histogram.

e.) Find the mean.

f.) Find the variance.

g.) Find the standard deviation

**
Problem # 9 (12 points)
**The mean cholesterol levels of women age 45-59 in Ghana, Nigeria, and

Seychelles is 5.1 mmol/l and the standard deviation is 1.0 mmol/l

Assume that cholesterol levels are normally distributed.

a.) State the random variable.

b.) Find the probability that a woman age 45-59 in Ghana, Nigeria, or Seychelles

has a cholesterol level above 6.2 mmol/l (considered a high level).

c.) Find the probability that a woman age 45-59 in Ghana, Nigeria, or Seychelles

has a cholesterol level below 5.2 mmol/l (considered a normal level).

d.) Find the probability that a woman age 45-59 in Ghana, Nigeria, or Seychelles

has a cholesterol level between 5.2 and 6.2 mmol/l (considered borderline

high).

e.) If you found a woman age 45-59 in Ghana, Nigeria, or Seychelles having a

cholesterol level above 6.2 mmol/l, what could you conclude?

f.) What value do 5% of all woman ages 45-59 in Ghana, Nigeria, or Seychelles

have a cholesterol level less than?

Problem # 10 ( 11 points)

In the United States, males between the ages of 40 and 49 eat on average 103.1 g

of fat every day with a standard deviation of 4.32 g (“What we eat,” 2012). The

amount of fat a person eats is normally distributed.

a.) State the random variable.

b.) Find the probability that a sample mean amount of daily fat intake for 35 men

age 40-59 in the U.S. is more than 100 g.

c.) Find the probability that a sample mean amount of daily fat intake for 35 men

age 40-59 in the U.S. is less than 93 g.

d.) If you found a sample mean amount of daily fat intake for 35 men age 40-59

in the U.S. less than 93 g, what would you conclude?

I have completed this assignment myself, working independently and not consulting anyone.

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