Normal Distribution Normal Distribution Bellshaped curve Symmetric Meanmedianmode

Normal Distribution

Normal Distribution • Bell-shaped curve • Symmetric • Mean/median/mode are the same in a perfectly normal distribution • The more data you collect the more “normal” the curve looks • Probability under curve is 100%

Normal Distribution

Normal Distribution for SAT Make a normal distribution curve for SAT scores. The mean is equal to 1500 and the standard deviation is 300.

Answer the following questions What percent of students receive a score between 1500 -1800? What percent of students receive a score between 900 -1500? What percent of students get a score of 900 or lower? If there are 320 students in the junior class at LBHS, how many students will score between 600 -1200? If there are 320 students in the junior class at LBHS, how many students will score above 2100?

Practice Problems 1. The speeds of cars on the highway have a mean of 75 m/h with a standard deviation of 5 m/h. What percentage of cars averaged less than 85 m/h? If a police car stopped cars that were going more than 80 m/h, how many cars would they stop if there were 8000 cars on the highway?

Practice Problems 2. A line up for tickets to a local concert had an average (mean) waiting time of 20 minutes with a standard deviation of 4 minutes. What percentage of the people in line waited for more than 28 minutes? If 2000 ticket buyers were in line, how many of them would expect to wait for less than 16 minutes?

Exit Ticket The monthly income of 5 000 workers at the Microsoft plant are distributed normally. Suppose the mean monthly income is $1250 and the standard deviation is $250. 1. How many workers earn more than $1500 per month? 2. What percentage of the workers earn between $750 and $1500 per month?

Z-score: how many standard deviations a data point is from the mean

Practice Problem The average number of hours teenagers spend on their phones is 9 hours a day, and the standard deviation is 2. If Pablo spends 6. 5 hours on his cell phone, what is his z-score? What would your z-score be?

Practice Problem Sara received a 77% on the last quiz, she knows the standard deviation is 4, and her z -score is 2. 8. What was the class average?

Practice Problem Find the standard deviation for our class averages for Unit 4 Test. 82%, 79%, 77% and 75%. What is Bri’s z-score if she scored 90? What is your z-score?

Exit Ticket Rommel is 5’ 9” and the standard deviation for height his age is 1. 7. He just learned that his z-score is 1. 32. What is the average height for Rommel’s age?