1. Warm Up
The weights of babies born in the “normal” range of weeks have been found to follow a roughly normal distribution.
Mean Std. Dev
Weight (grams)
1) What is the z-score for a baby born with a weight of 4000 grams? What proportion of babies have weights above 4000 grams?
2) What proportion of babies are born with weights between 7 pounds and 8 pounds (about 3200 and 3600 grams)?

2. Practice
Find the proportion of observations from a standard normal distribution that meet the following criteria:
< z < 0.75
Scores on the ACT are roughly normal with a mean of 20.9 and a standard deviation of 4.8.
a) If Hector scored a 24 on the ACT, what percentile is his score?
b) What score would he need to be in the 95th percentile?

3. Data Collection - Generating “Normal” Data
1) Everyone will flip a plastic spoon for a total of 50 flips. Make sure your spoon lands on the floor each time. On each flip record if the spoon lands “bowl up” or “bowl down” 2) Count the number of “bowl up” flips you have and write this number on the board. 3) We will see if the distribution of “bowl up” flips follows the behavior of a normal distribution.

4. Data Collection - Analyzing “Normal” Data
1) Calculate the mean and standard deviation for the data. 2) Make a histogram of the data and describe the shape of the distribution. 3) Assume the data is roughly normal. Based on your calculation of mean and standard deviation, what proportion of students should have gotten 18 or fewer “bowl up” flips? What proportion of students actually did? 4) Assume the data is roughly normal. Based on your calculation of mean and standard deviation, what proportion of students should have gotten 28 or more “bowl up” flips? What proportion of students actually did? 5) Is this data set roughly normal? Why or why not?

5. Practice
The gas tank for a certain car is designed to hold 15 gallons. Assume the distribution of the actual gas tank sizes is roughly normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons.
1) What proportion of the gas tanks hold between 14.8 and 15.2 gallons?
2) What proportion of the tanks hold more than 15.5 gallons?
3) The customer will not accept a tank that holds less than 14.6 gallons. What proportion of the gas tanks will be rejected by the customer?