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. Activity - Generating “Normal” Data
1) Everyone will roll 2 dice for a total of 20 rolls. On each roll record the total of the dice (if you roll a 5 and a 3 the total is 8). 3) Tally the number of rolls of each possible total (2-12) on the board. 4) We will add up the number of each possible total for the entire class.

4. Generating “Normal” Data
1) Record the number of rolls for each possible total for the entire class data set. Enter the value in L1 and the count in L2. 2) Calculate the mean and standard deviation for the data. I will show you how to do this on your calculator. 3) Make a histogram of the data and describe the distribution. 4) Assume the data is roughly normal. Based on your calculation of mean and standard deviation, what percentage of the rolls should be a 3 or lower? How many actually were? 5) Based on your calculation of mean and standard deviation, what percentage of the rolls should be a 10 or greater? How many actually were?

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?