AP Statistics HW: p95 22 – 24, 27 (skip part c) Obj: to understand and use a z-score and standard normal distribution Do Now: The mean monthly cost of gas is $125 with a standard deviation of $10. The distribution of the gas bills is approximately normal. a)What percentage of homes have a monthly bill of more than $115? b)Less than $115? c)What bill amount represents the top 16 percent? d)What bill amount represents the top 84% e)How many standard devations above the mean is a bill of $150? C2 D4

Z-Score (standardized value) Allows us to identify the position of a data value relative to the μ and σ of its set of data values. z = x – μ σ

Ex: If x = 13.75, μ = 10, and σ = 2.5, then the z-score = – This means that is 1.5 standard deviations above the mean of 10

Ex: If x = 100, μ = 120, and σ = 15, calculate the z-score and tell what it means.

If a variable x, which takes on the values x = {x 1, x 2, …, x n } has a normal distribution N(μ, σ) and we change every data value into its standardized score (z- score), this new variable z takes on the values z = {z 1, z 2, …, z n } and has the normal distribution N(0, 1) which we call the standard normal distribution

Standard Normal Dist’n

Ex: A student scores 625 on the math section of the SAT and a 28 on the math section of the ACT. She can only report one score to her college. If the SAT summary statistics include μ = 490 and σ = 100 and the ACT summary statistics include μ = 21 and σ = 6, which score should she report?

Ex: For data with a distribution N(0,1) calculate the following percentages: a)% of data values between -1 and 1. b)% of data values less than 1. c)% of data values greater than -1. d)% of data values less than 2. For what data values are 99.85% of the scores lower? Do p.95 #19, 20