1. Normal Distribution A common way that measured data is distributed. It is measured with the MEAN and STANDARD DEVIATION Symmetrical graph The Relative frequencies are always the same 34% 13.5% 2.35% 0.15% 2.35% 0.15% Pg 21

2. A group of students take a test and their scores follow a normal distribution with a mean of 85 and a standard deviation of 3. 1) what % of students scored higher than 91 on the test? 2) What % of students scored more than 85 on the test? 3) what % of students scored between 79 and 88 on the test? 4) 84% of the students scored above WHAT score? 34% 13.5% 2.35% 0.15% 2.35% 0.15% 76 79 82 85 88 91 94 Mean = 85 “Count by” St. Dev. = 3 These are the 2 sections to the right of 91 So 2.35 + 0.15 = 2.5% These are the 4 sections to the right of 85 So 34 + 13.5 + 2.35 + 0.15 = 50% These are the 3 sections between 79 and 88 So 13.5 + 34 + 34 = 81.5% #1 #2 #3 We are looking for scores ABOVE a certain value so count from the right Add up the % until you get to 84. 0.15 + 2.35 + 13.5 + 34 + 34 = 84% So 84% of the students scored above a 82 on the test #4

3. The mean height of trees in a forest is 65 feet, with standard deviation of 5 feet. 1.What % of trees are more than 55 feet tall? 2.What % of trees are between 60 and 75 feet tall? The score on the PSAT math test was 40 with standard deviation 12. 1.What % of scores were over 52? 2.What % of scores were less than 28? Adult IQ scores are normally distributed with mean 105 and standard deviation 15. 1.What % of adults have IQ over 35? 2.What % of adults have IQ between 75 and 135? The mean weight of apples in a barrel is 10 ounces with standard deviation 1.5 ounces. 1.What % of apples are less than 7.5 ounces? 2.2.5% of the apples are heavier than what weight?

4. The mean height of trees in a forest is 65 feet, with standard deviation of 5 feet. 1.What % of trees are more than 55 feet tall? 2.What % of trees are between 60 and 75 feet tall? The mean height of trees in a forest is 65 feet, with standard deviation of 5 feet. 1.What % of trees are more than 55 feet tall? 2.What % of trees are between 60 and 75 feet tall? The mean height of trees in a forest is 65 feet, with standard deviation of 5 feet. 1.What % of trees are more than 55 feet tall? 2.What % of trees are between 60 and 75 feet tall? The mean height of trees in a forest is 65 feet, with standard deviation of 5 feet. 1.What % of trees are more than 55 feet tall? 2.What % of trees are between 60 and 75 feet tall?

5. The mean speed of vehicle on a highway is 72 mph, with standard deviation of 3 mph. 1.What % of cars are traveling faster than 69mph 2.84 % of cars are slower than what speed? The mean time for runners in a 5K was 28 minutes with a standard deviation of 2 min. 1.What % of runners were faster than 24 minutes? 2.16% of runners were faster than what time? The heights of adult women have a mean of 65 inches and standard deviation of 1.5 inches 1.What % of women are over 68 inches? 2.97.5 % of women are taller than what height? The mean number of M&M’s in a bag is 42 with standard deviation of 1. 1.What % of bags have between 43-45 M&M’s? 2.84% of the bags have more than how many candies?

6. The mean score of a football game was 31 points with standard deviation 5 points. 1.What % of teams scored less than 21 points? 2.84 % of teams scored more than how many points? The mean height of corn in a corn maze is 96 inches with standard deviation of 5 inches. 1.What % of corn is below 86 inches tall? 2.16% corn is taller than what height? The heights of adult men have a mean of 72 inches and standard deviation of 2 inches 1.What % of men are over 68 inches? 2.97.5 % of men are shorter than what height? The mean number of kernels unpopped in a bag of popcorn is 35 with standard deviation of 3. 1.What % of bags have between 35-41 kernels? 2.84% of the bags have more than how many unpopped kernels?