# STA 2023 Florida Southwestern State College Statistical Methods Discussion

3/12/22, 8:53 AMTopic: Discussion #10 (sampling distribution of a proportion)

This is a graded discussion: 10 points possible
due Mar 20
Discussion #10 (sampling distribution of a proportion)
2
2
It is recommended that you complete this week’s MyLab Math assignments before you
submit this assignment.
For each discussion, students will post their answers to the question set.
Each question is worth 2 points.
Q1. A survey of 500 adults aged 18 – 29 years of age revealed that 285 chose to eat fast food for
dinner at least once in the past week. Find the sample proportion of individuals surveyed who ate
fast food for dinner at least once in the past week.
Q2. Determine
25,000.
and
from the given parameters. Assume the size of the population is
n = 200 p = 0.75
Q3. Sixteen percent of Americans do not have health insurance. Suppose a simple random
sample of 500 Americans is obtained. In a random sample of 500 Americans, what is the
probability that more than 20% do not have health insurance?
Q4. A simple random sample of size n=180 is obtained from a population whose size=20,000 and
whose population proportion with a specified characteristic is p=0.45. Determine whether the
sampling distribution has an approximate normal distribution. Show your work that supports your
conclusions.
Q5. Using the values in Q4, calculate the probability of obtaining x=72 or more individuals with a
specified characteristic.
HINT: remember to convert the number of individuals into a sample proportion
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3/12/22, 8:50 AM
Topic: Discussion #8 (normal probability distribution)

This is a graded discussion: 10 points possible
due Mar 12 at 11pm
10
Discussion #8 (normal probability distribution)
10
It is recommended that you complete this week’s MyLab Math assignments before you
submit this assignment.
For each discussion, students will post their answers to the question set.
Each question is worth 2 points.
Q1. Use the graph of the given normal distribution to identify μ and σ. (Read page # 331 of text
book)
Q2. Identify the two inflection points (read page #332 of text book) for the distribution in Q1.
Q3. Find the following probability of the standard normal random variable Z. (round to 4 decimal
places)
P(Z ≥ –2.31)
Q4. A pediatrician obtains the heights of her three year-old female patients. The heights are
approximately normally distributed, with mean 38.72 inches and SD 3.17 inches. Determine the
proportion of three-year-old females who have a height less than or equal to 35 inches. (round to
4 decimal places)
Q5. Find the z-score such that the area under the standard normal curve to the right is 0.10.
(round to two decimal places)
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3/12/22, 8:51 AM
Topic: Discussion #9 (sampling distribution of a mean)

This is a graded discussion: 10 points possible
due Mar 20
Discussion #9 (sampling distribution of a mean)
2
2
It is recommended that you complete this week’s MyLab Math assignments before you
submit this assignment.
For each discussion, students will post their answers to the question set.
Each question is worth 2 points.
Q1. Determine
and
from the given population parameters and the sample size.
μ = 84 σ = 12 n = 30
Q2. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is
the probability a random sample of 20 people have a mean IQ score greater than 110?
Q3. Home sizes in Anytown, USA have a mean of 2400 square feet and a standard deviation of
450 square feet. What is the probability that a random sample of 50 homes in Anytown, USA has
a mean square footage less than 2200 square feet?
Q4. In your own words, what does the central limit theorem tell us? (Page #373 of text book)
Q5. A simple random sample of size n=40 is obtained from a population with
Does the population distribution need to be normally distributed for the sampling distribution of
to be approximately normally distributed? Why or why not? What is the mean and standard
deviation of the sampling distribution?
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