MATH 225N Week 5 Assignment: Central Limit Theorem for Means.

MATH 225N Week 5 Assignment: Central Limit Theorem for Means. 1. Question A family of statisticians is trying to decide if they can afford for their child to play youth baseball. The cost of joining a team is normally distributed with a mean of $750 and a standard deviation of $185 . If a sample of 40 teams is selected at random from the population, select the expected mean and standard deviation of the sampling distribution below. Correct answer: σx¯=$29.25 μx¯=$750 The standard deviation of the sampling distribution σx¯=σn−−√=$18540−−√=$29.25 When the distribution is normal the mean of the sampling distribution is equal to the mean of the population μx¯=μ=$750 . Question A cupcake baker is planning a supplies order and needs to know how much flour he needs. He knows that his recipes use an average of 100 grams of flour, normally distributed, with a population standard deviation of 15 grams. If he is consulting a sample size of 30 recipes, select the mean and standard deviation of the sampling distribution to help him order his supplies from the options below. σx¯=2.74 grams μx¯=100 grams The standard deviation of the sampling distribution is σx¯=σn−−√=1530−−√=2.74 grams Likewise, when the distribution is normal the mean of the sampling distribution is equal to the mean of the population μx¯=μ=100 grams. Question A head librarian for a large city is looking at the overdue fees per user system-wide to determine if the library should extend its lending period. The average library user has $19.67 in fees, with a standard deviation of $7.02 . The data is normally distributed and a sample of 72 library users is selected at random from the population. Select the expected mean and standard deviation of the sampling distribution from the options below. Correct answer: σx¯=$0.83 μx¯=$19.67 The standard deviation of the sampling distribution is σx¯=σn−−√=$7.0272−−√=$0.83 When the distribution is normal, the mean of the sampling distribution is equal to the mean of the population μx¯=μ=$19.67 . 2. Question