# STAT 250 Data Analysis Assignment 3

August 30, 2017

Question
Data Analysis Assignment 3: Due Friday 11/06/15 by 11:59 PM
Make sure you do the following:
2. Under your name, put STAT 250 with your correct section number (e.g. STAT 250-0xx)
3. Type Data Analysis Assignment 3 centered on Page 1.
4. Number and letter the answers accordingly and keep the problems in order.
5. Use complete and coherent sentences to answer the questions.
6. Please title and label all of your graphs correctly (as we learned to do in class).

Problem 1: Heights of Females* (see end of document for more information)
Heights of females are known to follow a normal distribution with mean 64.5 inches and
standard deviation 2.8 inches. Based on this information, answer the following questions.
a) Find the probability that a randomly selected female is taller than 67 inches. Draw a
picture, shade area, standardize, and use Table 2 to obtain this probability. Please take a
answer using a StatCrunch normal graph. Copy that image into your document as well.
b) Find the proportion of females who are between 60 and 62 inches tall (use only a
StatCrunch graph).
c) Find the maximum height that would put a female in the bottom 4% of all female heights.
Draw a picture, shade area, standardize, and use Table 2 to obtain this probability. Please
well.
Problem 2: Grading on a Bell Curve
The mean and standard deviation of last semester’s Exam 1 scores were 75.43 and 16.74
respectively. Imagine I wanted to define letter grades using a normal distribution (assuming this
is appropriate). One possible grade distribution could be that the lowest 5% of students to earn
Fs, the next 10% earn Ds, the next 35% earn Cs, the next 25% earn Bs, and the rest of the
students earn As. Provide the Exam 1 scores that would separate these letter grades using the
normal distribution. Your answer needs to be five normal graphs in StatCrunch where each
shaded area on each graph shows the range of scores needed to earn the specific letter grade.
Hint: the graphs for A and F will only have one value as a cutoff score whereas the graphs for a
D, C, and B will have two cutoff scores (a low and a high score for that particular grade).
Problem 3: Common Last Names

The Census Bureau says that the 10 most common last names in the United States are (in order)
Smith, Johnson, Williams, Jones, Brown, Davis, Miller, Wilson, Moore, and Taylor. These
names account for 5.6% of all US residents. Consider our class as a random sample of 18
individuals.
a) Check if this situation fits the binomial setting.
b) Assuming it does, build the probability distribution as a table in StatCrunch. For your
probability distribution table, since the probabilities will be very close to 0 after about X
= 7, you may cut off the table after 7.
c) Find the probability that exactly 2 individuals have one of those last names. Provide a
d) Calculate the probability that at least one individual has one of those last names. Again,
e) Calculate the probability that between 3 and 5 individuals (inclusive) have one of those
last names. Use the probability distribution to answer this question (then verify it with a
StatCrunch graph.
f) Find the mean and standard deviation of this probability distribution (you may use the
binomial mean and standard deviation formulas in the notes).
Problem 4: Building a Sampling Distribution
Use my StatCrunch data set to build the sampling distribution of the sample proportion of
college student’s approval rating as we did in class (the data set is titled Opinions of 35,000
College Students Concerning the President and is posted in our StatCrunch group). This time,
take 10,000 samples of size 50 and choose to display the sample proportion from each of the
10,000 samples. Give your computer a chance to collect the data; this may take up to 3 minutes.
Be patient.
a) Graph the results in a histogram and discuss the shape, center, and spread.
b) Check the conditions of the central limit theorem and use the theorem to define the
sampling distribution’s shape, mean, and standard deviation and compare it to your
histogram.
c) Lastly, for the defined sampling distribution, provide the probability that in a random
sample of size 50, more than the majority supports the president.
Problem 5: Got Milk

According to the U.S. Department of Agriculture, 58.8% of males between 20 and 39 years old
consume the minimum daily requirement of calcium. After an aggressive “Got milk” advertising
campaign, the USDA conducted a survey of 55 randomly selected males between the ages of 20
and 39 and found that 36 of them consume the recommended daily allowance of calcium.
a) Construct a 99% confidence interval for the above data. Show your work using the
formulas and verify your work using StatCrunch.
b) Interpret this confidence interval as we learned in class.

Note: To add formulas to a Word document, go above to Insert object Microsoft Equation 3.0.
You can also copy and paste the following formulas when you need them (double click on the
formula to replace the letters with numbers).
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p z *

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p1 p
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