Download Sampling Distribution with CLT Worksheet

AP Stats: Ch 9 Sampling Distribution with CLT Practice
1. A sample is chosen randomly from a population that can be described as normally distributed.
a) What is the sampling distribution shape, center, and spread compared to the population?
b) If we choose a larger sample, what is the effect on this sampling distribution? What stays the
same, what changes and how?
2. A sample is chosen randomly from a population that is strongly skewed right, …
a) Describe the sampling distribution for sample mean if the sample size was small.
b) As we make the sample size larger, what will happen to the expected sampling distribution of
sample mean’s shape, center, and spread compared to the population’s.
3. M&M’s claims 20% of the candies it produces is red. Suppose that the candies are packaged at
random in small bags containing about 50 M&M’s. A class of elementary school students learning
about percents opens several bags, counts the red candies, and divides the count by the sample size of
50 candies, and calculates the proportion that are red.
a) If we plot a histogram showing the proportions of red candies in the various bags, what shape
would you expect it to have?
b) Can that histogram be approximated by a normally distributed sampling distribution? Explain
how you know (verify). Why is this important? What does it tell us?
c) Where should the center of the histogram be?
d) What should the standard deviation of the sampling proportion distribution be?
4. State police believe that 70% of the drivers traveling on I-10 exceed the speed limit. They plan to set
up a radar trap and check the speeds of 80 cars.
a) What is the expected proportion of speeding cars?
b) What is the standard deviation of the proportion of speeding cars?
c) Verify if the appropriate conditions are met.
d) If conditions have been met (which they should have), sketch and label a normal distribution
with mean and standard deviation based on the sample of 80 cars.
e) What percent (probability) of the time will state police find more than 60 of the drivers
speeding (Hint: 60 of 80 is equivalent to 75%)?
5. A college’s data about incoming freshmen indicates that the mean of their high school GPAs was 3.4
with a standard deviation of 0.35; the distribution was roughly mound-shaped and only slightly
skewed. The students are randomly assigned to freshman writing seminars in groups of 25.
a) What might the mean GPA of one group of these seminar groups be?
b) What is the approximate standard deviation of GPA of one group of these seminar groups?
c) Describe the appropriate shape of the sampling distribution of GPA of one group.
d) Is a sample size of 25 sufficiently large enough? Explain.
e) Sketch and label the sampling distribution of GPAs of one group.
f) What is the likelihood that one group would have a GPA mean less than 3.26?
6. Some business analysts estimate that the length of time people work at a job has a mean of 6.2 years
and a standard deviation of 4.5 years.
a) Explain why you suspect this distribution may be skewed to the right.
b) Explain why you could estimate the probability that 100 people selected at random had
worked for their employers an average of 10 years or more, BUT you could not estimate the
probability that an individual had done so. (Do not calculate probability—simply answer the
question).