Day 2: Using Technology. Unit 1: Sta5s5cs

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1 Day 2: Using Technology Unit 1: Sta5s5cs

2 Have out your homework and homework stamp sheet Warm Up Reminder: The z- score is the number of standard devia7ons a value is away from the mean. The mean speed of vehicles along a stretch of highway is 56 mph with a standard devia;on of 4 mph. You measure the speed of three cars traveling along this stretch of highways as 62 mph, 47 mph, and 56 mph. Find the z- score that corresponds to each speed. 10 minutes End

3 Homework Check 3. The height of women aged 20 to 29 are approximately normal with mean 64 inches and standard devia5on 2.7 inches. Men the same age have mean height 69.3 inches with standard devia5on 2.8 inches. John and his sister June both play basketball for N. C. State University. John is 81 inches tall; June is 74 inches tall. (a) Compared to their respec5ve peers, who is the tallest? (b) How tall would a woman be who has a z- score of 1.5? (c) If a man has a z- score of and a woman has a z- score of 1.2, which is tallest?

4 Homework Check 1. The mean score on the midterm was an 82 with a standard devia5on 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

5 Homework Check 2. The mean SAT score is 490 with a standard devia5on of 100. Find the probability that a randomly selected student: a. scored between 390 and 590 b. scored above 790 c. scored less than 490 d. scored between 290 and 490

6 The Empirical Rule In sta5s5cs, the rule, also known as the Empirical Rule, states that nearly all values lie within three standard devia5ons of the mean in a normal distribu5on.

7 68% of the data falls within ± 1σ 68%

8 95% of the data falls within ± 2σ 95%

9 99.7% of the data falls within ± 3σ 99.7%

10 When you break it up.15% 13.5% 34% 34% 13.5%.15% 2.35% 2.35%

11 How do you use this? The scores on the Math 3 midterm were normally distributed. The mean is 82 with a standard devia5on of 5. Create and label a normal distribu5on curve to model the scenario. Draw the curve, add the mean, then add the standard devia5ons above and below the mean.

12 Draw the curve, add the mean, then add the standard devia5ons above and below the mean..15% 13.5% 34% 34% 13.5%.15% 2.35% 2.35%

13 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 68% 34% 81.5% d. scored higher than 92 e. scored less than % 16%

14 Classwork In your groups, complete the right side of yesterday s handout. Time Keeper: 10 minutes Reader: Read each ques5on

15 Today s Objec;ves 1. Review z- scores and empirical rule 2. Use technology to calculate probabili5es in a normal distribu5on

16 Review: Z- score The grades on a Math 3 midterm at KHS are normally distributed with μ = 74 and σ = 3.0. Ben scored 73 on the exam. Find the z- score for Ben's exam grade. Round to two decimal places.

17 Review: Percentages What is the mean? Standard Devia5on? The data below is normally distributed. What percentage of the values lie between 33 and 45?

18 Challenge What is wrong with this diagram?

19 You might be wondering what happens if you re looking for probabili5es that are not perfect standard devia5ons away from the mean? normalcdf (lower, upper, µ, σ) How to find: 2 nd + VARS, 2:normalcdf(

20 The scores on the CCM3 midterm were normally distributed. The mean is 82 with a standard devia5on of 5. a. What s the probability that a randomly selected student scored between 80 and 90? normalcdf (80, 90, 82, 5) = or 60.06% b. What s the probability that a randomly selected student scored below 70? normalcdf (0, 70, 82, 5) = or.82% c. What s the probability that a randomly selected student scored above 79? normalcdf (79, 100, 82, 5) = or 72.56%

21 You can also work backward to find percen5les! d. What score would a student need in order to be in the 90 th percen5le? 90 th Percen5le invnorm (percent of area to leo, µ, σ) invnorm (0.9, 82, 5) = 88.41, or 89

22 e. What score would a student need in order to be in top 20% of the class? invnorm (0.8, 82, 5) = 86.21, or 87

23 The average wai5ng 5me at Walgreen s drive- through window is 7.6 minutes, with a standard devia5on of 2.6 minutes. When a customer arrives at Walgreen s, find the probability that he will have to wait a. between 4 and 6 minutes b. less than 3 minutes c. more than 8 minutes d. Only 8% of customers have to wait longer than Mrs. Jones. Determine how long Mrs. Jones has to wait minutes

24 Questions about normal distribution?

25 Group Work Work in your groups to complete 8 problems about Normal Distribu5on. Draw your curves and write your answers on a separate piece of paper. Be prepared to share with the class. Resource Manager: Obtain a worksheet for each person Reader: Read each ques5on out loud Time Keeper: 20 minutes Spy Monitor: Check in with other groups

26 Homework HW 1.2 Normal Distribu5on Quiz Friday!

Pre-AP Geometry Course Syllabus Page 1

Pre-AP Geometry Course Syllabus 2015-2016 Welcome to my Pre-AP Geometry class. I hope you find this course to be a positive experience and I am certain that you will learn a great deal during the next