M3U9D2 Warm-up: 1. At the doctor’s office, there are three children in the waiting room. The children are ages 3, 4, and 5. Another 4 year old child enters.

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Presentation transcript:

M3U9D2 Warm-up: 1. At the doctor’s office, there are three children in the waiting room. The children are ages 3, 4, and 5. Another 4 year old child enters the room. a)What will happen to the mean of the children’s ages when the new child enters? When the new child enters, nothing will happen to the mean because the child’s age is the mean of the set. b) What will happen to the standard deviation of the children’s ages? The standard deviation will decrease because the 4 th value is exactly equal to the mean, which will give the data less variability than originally

HW Check: 1) systematic 2) cluster 3) stratified 4) cluster 5) voluntary response 6) convenience 7) stratified 8) cluster 9) convenience 10) simple random 11) stratified 12) systematic 13) simple random 14) cluster

How do you find the mean? Add numbers together then divide by the number of entries What is standard deviation? How much variation from the average exists.

M3U9D2 Normal Distribution and the Empirical Rule Objective: To fit a data set to the normal distribution using the mean and standard deviation AND To apply the Empirical Rule to estimate probabilities for normal distributions

Normal Distributions Sampling and Study Design Estimating Population Parameters

Normal Distributions Video

Characteristics of a normal distribution: 1. Continuous random variable 2. Symmetric with respect to the mean 3. mean = median = mode 4. Area under the curve is 1 YOU should know these characteristics!

The Standard Normal Curve… Z-score: number of standard deviations a value is from the mean on the standard normal curve µ = 0; σ = 1

What is the meaning of a positive z-score? What about a negative z-score?

How do you use this? The mean score on the SAT is 1500, with a standard deviation of 240. The ACT, a different college entrance examination, has a mean score of 21 with a standard deviation of 6. If Bobby scored 1740 on the SAT and Kathy scored 30 on the ACT, who scored higher?

Bobby Kathy z = 1z = 1.5 What should a complete answer look like? Correct mathematical work Interpretation of that work in context of the problem

For example: Kathy scored higher than Bobby overall – her z-score on the ACT shows that she scored 1.5 standard deviations above the mean while Bobby scored only 1 standard deviation above the mean on the SAT.

68% of the data falls within ± 1 σ

95% of the data falls within ± 2 σ

99.7% of the data falls within ± 3σ

When you break it up…

The scores on the Math III midterm were normally distributed. The mean is 82 with a standard deviation of 5. Find the probability that a randomly selected person: a. scored between 77 and 87 b. scored between 82 and 87 c. scored between 72 and 87 d. scored higher than 92 e. scored less than 77 How do you use this?

Draw the curve, add the mean, then add the standard deviations above and below the mean…

a. scored between 77 and 87 b. scored between 82 and 87 c. scored between 72 and 87 d. scored higher than 92 e. scored less than 77 68% 34% 81.5% 2.5% 16%

Sleep Activity 2 nd, Vars (DISTR), Normalcdf Normalcdf(min,max,mean,st dev) Gives % 2 nd, Vars (DISTR), InvNorm InvNorm(%, mean, st dev) Gives a boundary

Classwork: U9D2 The Normal Distribution & distribute calculator directions Homework: U9D2 Using the Empirical Rule WS