1. Warm Up
A recent study found that 79% of U.S. teens from years old use Snapchat. Suppose samples of 100 U.S. teens from years old are taken. 1) What is the mean and standard deviation of the sampling distribution of the proportion of U.S. teens using Snapchat in a sample size of 100? 2) Is it reasonable to use a normal approximation for the sampling distribution? 3) Find the probability that a sample proportion will be less than 0.70.

2. Example
The heights of adult men follow a roughly normal distribution with a mean of 69.5 inches and a standard deviation of 2.5 inches. 1) FInd the probability of choosing one man at random and his height is more than 6 feet. 2) Find the probability of choosing 10 men at random and their mean height is more than 6 feet.

3. Practice
A hot dog manufacturer claims their dogs contain on average 18 grams of fat and follow a normal distribution with a standard deviation of 1.1 grams. A researcher randomly selected 36 hot dogs and found the sample mean to be 18.4 grams of fat. How likely is the researcher to get a result of 18.4 grams or higher if the manufacturer’s claims are true?

4. Digits in Your Phone Number
1) Make a tick mark under the correct number (0-9) for each of the last 4 digits of your cell phone number. This will be our population. 2) Make a histogram of the data. Comment on the distribution (SOCS). Is the distribution roughly normal? 3) Find the mean and standard deviation for our population (Use L1 and L2 on your calculator. L1 is the value and L2 is the frequency).

5. Sampling Distribution of Sample Means
1) First Sample: Combine the last 4 digits of you and your partner’s number. Find the mean of this sample and write it under the correct digit on the board. 2) Second Sample: Write each of the last 4 digits of your phone number on a separate scrap of paper. When told to do so, trade one of your numbers with someone from another table. Do not trade with anyone at your table. You must trade all of your numbers. Combine the last 4 digits of the “new” number for you and your partner. Find the mean of this sample and write it under the correct digit on the board. 3) Third Sample: When told to do so, repeat step #2

6. Digits in Your Phone Number
1) Make a histogram of the “sampling distribution of sample means.” Calculate the mean and standard deviation of the “sampling distribution.” 2) Compare and contrast the distribution of the population to the “sampling distribution” (n = 8). 3) Compare the mean and standard deviation of the population to the “sampling distribution.”

7. Practice
A 2009 study found that the length of the courtship dance among mating scorpion flies has a mean of minutes with a standard deviation of minutes. Obviously the distribution of courtship dance lengths is not normal.
1) Assume numerous samples of 20 couples were taken.
What is the mean and standard deviation of the length of the mating dance for this sampling distribution?
What is the probability the mean length of the mating dance for a sample of 20 couples is less than 100 minutes?
2) Repeat question 1) for samples of 50 couples.