Assuming a normal distribution… Find the area to the left of 𝑧= 1.73 Find the area between 𝑧=−1.5 and 𝑧 = 1.5 Estimate the probability of a value having a z-score higher than 2.21 1) 0.9582 2) 0.8664 3) 1.355% or 0.01355
Sec. 5.3 Finding Probabilities Using Normal Distributions Mr. Ricks Madison High School
A survey indicates that people use their computers an average of 2 A survey indicates that people use their computers an average of 2.4 years before upgrading. If the standard deviation is 0.5 years, estimate the probability that a randomly selected computer user will use their computer for 1 year or less before upgrading. (Assume a normal distribution) Apply what we know about normal distributions to solve this problem on the board with your team. About 0.002555 or 0.2555%
General Strategies Convert Raw Values To Standard Values (z-scores) Sketch a normal distribution and shade the region you are interested in Use table in book or calculator to find probability
A 2015 Ford Focus reportedly gets an average of 29 mpg in city driving A 2015 Ford Focus reportedly gets an average of 29 mpg in city driving. Assuming a normal distribution and a standard deviation of 1.6 mpg, estimate the probability that a randomly selected Focus gets more than 30 mpg for city driving. 26.60% or 0.2660
A survey indicates that for each trip to the supermarket, shoppers spend an average of 45 minutes shopping with a standard deviation of 12 minutes. Estimate the probability that the shopper is in the store between 33 and 60 minutes. If 2000 shoppers enter the store on a given day, estimate how many of them will spend less than 15 minutes in the store. 73.57% 12-13
Sec. 5.4 Finding Various Values Using a Normal Distribution Mr. Ricks Madison High School
Finding a z-score Given an Area Find the z-score that corresponds to a cumulative area of 0.0384 Table: Find area in table and identify corresponding z-score Calculator: 2ndDISTR3, input area Find the z-score that corresponds to a cumulative area of 0.9901
Finding a z-score Given a Percentile P5 represents the 5th percentile, P30 represents the 30th percentile, etc. Recall that the area correlates to the percentile so for P5 we are looking for the z-score that gives us 5% of the area
Find the Z-score that corresponds to each of the following percentiles.
Transforming a z-score to an x-Value Sometimes we have a z-score, and we’d like to know what data value it corresponds to 𝑧= 𝑥−𝜇 𝜎 What does each symbol represent? We will rearrange this equation to solve for ____ 𝑥=𝜇+𝑧𝜎
Monthly utility bills in a city have a mean of $70 and a standard deviation of $8. Find the x-values that correspond to z-scores of… -0.75 4.29 -1.82
Finding a Data Value for a Given Probability The braking distances of a sample of Ford F-150s are normally distributed. On a dry surface, the mean braking distance was 158 feet and the standard deviation was 6.51 feet. What is the longest braking distance one of these trucks could have and still be in the best 1%? About 143 feet
The length of time employees have worked at a corporation is normally distributed with a mean of 11.2 years and a standard deviation of 2.1 years. In a company cutback the lowest 10% in seniority are laid off. What is the maximum length of time and employee could have worked and still be laid off? About 8.5 years
Sec. 5. 3-5. 4 Pg. 225 #1-19 (odd), 2 pts. each (10 questions) Pg Sec. 5.3-5.4 Pg. 225 #1-19 (odd), 2 pts. each (10 questions) Pg. 234 #1-39 (odd), 2 pts. each (20 questions)