SWBAT: 5.2 -Calculate probabilities for normally distributed variables using a table or technology 5.3 -Calculate a z-score given the area under the curve.

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Presentation transcript:

SWBAT: 5.2 -Calculate probabilities for normally distributed variables using a table or technology 5.3 -Calculate a z-score given the area under the curve -Transform a z-score to an x-value -Calculate a specific data value of a normal distribution given the probability Agenda: -Review homework -Notes -Assign homework

Normal Distributions: Finding Probabilities If a random variable x is normally distributed, you can find the probability that x will fall in a given interval by calculating the area under the normal curve for the given interval

The weights of adult male beagles are normally distributed, with a mean of 25 pounds and a standard deviation of 3 pounds. A beagle is randomly selected. a.Find the probability that the beagle’s weight is less than 23 pounds a.Find the probability that the beagle’s weight is between than 24.5 and 25 pounds c. Find the probability that the beagle’s weight is more than 30 pounds..0478

Normal Distributions: Finding Values Finding Z-scores given a probability or area under the curve a.Find the z-score that corresponds to a cumulative area of b.Find the z-score that has 10.75% of the distribution's area to its right c.Find the z-score for P

Example 1: A veterinarian records the weights of dogs treated at a clinic. The weights are normally distributed, with a mean of 52 pounds and a standard deviation of 15 pounds. Find the weights x corresponding to z-scores of -2.33, 3.10, and Z score: x = x = 98.5 x = 60.7

Example 2: The braking distances of a sample of Nissan Altimas are normally distributed with a mean of 129 feet and a standard deviation of 5.18 feet. What is the longest braking distance one of these Nissan Altimas could have and still be in the bottom 1%? 2 nd Vars -> invNorm feet

Example 3: Scores by the California Peace Officer Standards and Training test are normally distributed with a mean of 50 and a standard deviation of 10. An agency will only hire applicants with scores in the top 10%. What is the lowest score you can earn and still be eligible to be hired by the agency? 62.8

Homework Pg 252 # 10–26 even Pg 262 # 4-40 every 4th