Probability of Average Charge Times and In-City Mileage with Normal Distribution - Prof. S, Assignments of Statistics

Download Probability of Average Charge Times and In-City Mileage with Normal Distribution - Prof. S and more Assignments Statistics in PDF only on Docsity! NAME STAT 269 - Introductory Statistics Examples using the Normal Distribution for Samples 1. Assume the length of time between charges of a cellular phone is normally distributed with a mean of 10 hours and a standard deviation of 1.5 hours. Suppose that a family has four cell phones. Find the probability that the average charge times for the four cell phones when each are observed for one random period phone will be between 9 and 11 hours. 2. Suppose an automobile manufacturer introduces a new model that has an advertised mean in-city mileage of 27 miles per gallon. Although such advertisements seldom report any measure of variability, suppose you are able to discover that the standard deviation is 3 miles per gallon. Assume that the distribution is approximately normal. What is the probability that a eet of 20 randomly purchased car will average less than 25 miles per gallon for in-city driving? Would getting less than 25 miles per gallon on average for this eet cause you to doubt the accuracy of their claim? 3. Suppose the scores on a college entrance examination are normally distributed with a mean of 550 and a standard deviation of 100. A certain department at a prestigious university would like to claim that the average score for their 50 rst-year students exceeds the 99th percentile of the distribution of average scores for all possible groups of 50 randomly selected students. Find the minimum score their students must achieve, on average, in order to validate this claim.