Statistics 5.2: Normal Distributions—Finding Probabilities
Objective: I can find probabilities for normally distributed variables.
If a random variable x is from a normal distribution, we can find the ______that x will fall in a given interval by finding the ______.
Read pg 253.
1) Convert any given x-value(s) into ______using the formula:
2) Use the standard normal table to find any area(s) to the ______of the z-scores.
3) State the correct decimal answer for the needed area. You can use decimals or percents.
*Recall that to find area to the right of a given value,
*Recall that to find area between two values,
Ex 1: A survey indicates that people use their computers an average of 2.4 years before upgrading to a new machine. The standard deviation is 0.5 year. A computer owner is selected at random. Find the probability that he or she will use it for fewer than 2 years before upgrading. Assume that the variable x is normally distributed.
TIY 1: A Ford Focus manual transmission gets an average of 24 miles per gallon (mpg) in city driving with a standard deviation of 1.6 mpg. A Focus is selected at random. What is the probability that it will get more than 28 mpg? Assume that gas mileage is normally distributed.
Ex 2: A survey indicates that for each trip to the supermarket, a shopper spends an average of 45 minutes with a standard deviation of 12 minutes in the store. The length of time spent in the store is normally distributed and is represented by the variable x. A shopper enters the store.
A) Find the probability that the shopper will be in the store from 24 to 54 minutes.
B) Find the probability that the shopper will be in the store for more than 39 minutes.
C) If 200 shoppers enter the store, about how many would you expect to be in the store for each time interval above?
Ex 3: Assume that cholesterol levels in men in the United States are normally distributed with a mean of 215 milligrams per deciliter () and a standard deviation of 25 . You randomly select a man from the Unites States. What is the probability that his cholesterol level is less than 175 ?