6.2 Areas under the curve 2018.notebook January 18, 2018

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1 More details about z scores * A z score is the number of standard deviations between a measurement and its mean. * Use z scores to make comparisons of measurements from different distributions (if the distributions have different means and/or standard deviations. * Z scores can be positive, negative or zero. positive indicates the measurement is above the mean (to the right of zero on the curve) negative indicates the measurement is below the mean (to the left of zero on the curve) Students will be able find areas under the standard normal curve to answer How to read z scores on the chart. Remember that the area under the curve is the probability! When you look up a z score the number is telling you the area to the left of that number. 3 Situations: 1) Find the area under the curve to the left of a given z value. Read straight off of the chart: ex) find the area left of z = 1.82 (same as find the probability of z < 1.82) draw: estimate: look up: ex) find the area left of z = 2.35(same as find the probability of z < 2.35) draw: estimate: look up:

2 2) Find the area under the curve to the right of a given z value. option 1: 1 Area value to the left of z option 2: Area to the right of z = Area to the left of z ex) find the area to the right of z = 1.30 P (z > 1.30) draw: estimate: subtract look up the number in the chart: 1 # from the chart ex) find the probability that z > Find the area to the right of z = 2.75 draw: estimate: subtract look up the number in the chart: 1 # from the chart 3) Find the area between two z values. Area to the left of large z value Area to the left of small z value large # from the chart small # from the chart ex) Find the area between z = 1 and z = 2.30 draw: estimate: look up both numbers: large small x) Find probability P( 1.78 < z < 0.35) draw: estimate: look up both numbers: large small

Summary the probability can be found: 1. If less than (shaded to the left) Read directly from the chart. 2. If more than (shaded to the right) 1 number from the chart. 3.

3 Summary the probability can be found: 1. If less than (shaded to the left) Read directly from the chart. 2. If more than (shaded to the right) 1 number from the chart. 3. If between 2 values large # from chart small # from chart Putting together the pieces Normal Distribution with µ = 10, σ=2 Find the probability that an x selected at random is between 11 and 14 first decide if the emperical rule can answer this question. 11 < x < 14 For x = 11, For x = 14, < z <

4 6.2 Areas under the curve 2018.notebook January 18, 2018

period of 2 years P(x 2) sketch estimation chart value Style it hair dryer's have a mean life span of 3.5 years with a standard deviation of.9 of a year.

5 Nordik's motor scooters have an average life of 2.3 years with standard deviation of 0.4 years. What is the probability that a motor scooter will break down during the warranty first decide if the emperical rule can answer this question. period of 2 years P(x 2) sketch estimation chart value Style it hair dryer's have a mean life span of 3.5 years with a standard deviation of.9 of a year. If they offer a 3 year warranty (to repair or replace the hair dryer) how many hair dryer's should they expect to be repairing/ replacing? first decide if the emperical rule can answer this question. P(x 3) sketch estimation chart value

Students will be able to change a normal curve into a standard normal curve and find areas under the standard normal curve to answer To convert the given z values to x values.

6 Students will be able to change a normal curve into a standard normal curve and find areas under the standard normal curve to answer To convert the given z values to x values. ex) The amount of cheese required for a large pizza has a mean of 8 oz. with a standard deviation of 0.5 oz. The franchise will be shut down if the amount of cheese for a large pizza is three standard deviations below the mean. One way to find out the minimum amount is to change the z score to an x value. z = 3 (3 standard deviations below the mean) x = zσ + μ or If your z score on the college entrance exam is 1.3. If the raw scores have a mean of 480 and a standard deviation of 70 points, what is your raw score? x = zσ + μ page 319 (1,2 a,b,c,3 a,b,e,f odd, 25,29,31,33,37,41,47) MUST SHOW CURVE WITH SHADING AND ANSWER FOR CREDIT! page 306 (14B) When finished AND checked be sure Mrs.Cohen approves it and writes your grade down. Khan Academy AND chapter 6b test are both on Wed. Feb. 1st. (2 weeks from today) you need to be keeping up with Khan Academy. NO RETAKES ON KHAN ACADEMY!!! ONLY ALLOWED TO RETAKE ONE STATISTICS TEST.

Normal Curves and Sampling Distributions

Normal Curves and Sampling Distributions 6 Copyright Cengage Learning. All rights reserved. Section 6.2 Standard Units and Areas Under the Standard Normal Distribution Copyright Cengage Learning. All rights