[Top Answer] MATH225N – Week 5 Assignment Central Limit Theorem for Means

Description

Week 5: Normal Distribution

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Week 5 Assignment – Central Limit Theorem for Means

Activity 1

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.

Select all that apply:

• σx¯=$7.02
• σx¯=$0.10
• σx¯=$0.83
• μx¯=$0.27
• μx¯=$2.80
• μx¯=$19.67

Answer

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Activity 2

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.

• σx¯=$185
• σx¯=$29.25
• σx¯=$4.63
• μx¯=$118.59
• μx¯=$18.75
• μx¯=$750

Answer

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Activity 3

Question

A well known social media company is looking to expand their online presence by creating another platform. They know that they current average 2,500,000 users each day, with a standard deviation of 625,000 users. If they randomly sample 50 days to analyze the use of their existing technology, identify each of the following, rounding to the nearest whole number if necessary:

Answer

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Activity 4

Question

A bank is reviewing its risk management policies with regards to mortgages. To minimize the risk of lending, the bank wants to compare the typical mortgage owed by their clients against other homebuyers. The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500. Suppose a random sample of 150 Americans is selected.

Identify each of the following, rounding your answers to the nearest cent when appropriate:

Answer

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Activity 5

Question

The average time it takes a certain brand of ibuprofen to start working is 25 minutes, with a standard deviation of 13 minutes, distributed normally. A pharmacist randomly samples 20 pills from this brand, because she is researching different brands in order to find the quickest acting ibuprofen to recommend to her customers. Identify the following to help her make her recommendations, rounding to the nearest hundredth if necessary:

Answer

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