Download 6 - Harmony

11.5 (New Book) Notes AM
Date: __________________________________
Goal: Understand how to identify and analyze normal probability distributions.
I. Normal Distributions
Criteria for
Normal
Distribution
The Empirical
Rule
Ex. A normal distribution has a mean of 21 and a standard deviation of 4
A. Find the range of values that represent the middle 68% of the distribution.
B. What percent of the data will be greater than 29?
Ex. A normal distribution has a mean of 8.2 and a standard deviation of 1.3
A. Find the range of values that represent the middle 95% of the distribution.
B. What percent of the data will be less than 4.3%?
Ex. The heights of 1800 adults are normally distributed with a mean of 70 inches and a standard deviation of 2 inches.
A. About how many adults are between 66 and 74 inches?
B. What is the probability that a random adult is more than 72 inches tall?
Ex. The number of friends per member in a sample of 820 members is normally distributed with a mean of 38 and a
standard deviation of 12.
A. About how many members have between 26 and 50 friends?
B. What is the probability that a random member will have more than 14 friends?
Z-test
Ex. Find z if X  18, X  22,s  3.1
Ex. Find X if z  0.73, X  39,s  8.2
Standard
Normal
Distribution
Ex. The number of videos uploaded daily to a video-sharing site is normally distributed with X  181,099 videos and
s  35,644 videos. Find each probability and use a graphing calculator to sketch corresponding area under the curve.
A. P(180,000  x  200,000)
B. P(X  250,000)
Ex. The life spans of a certain tread of tire are normally distributed with X  31,066 videos and s  1644 videos. Find each
probability and use a graphing calculator to sketch corresponding area under the curve.
A. P(30,000  x  32,000)
B. P(X  35,000)
11.5 HW: 1-17odd