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# (Solved) MATHH225 Week 5 Assignment Central Limit Theorem for Means

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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 ofÂ \$750Â and a standard deviation ofÂ \$185. If a sample ofÂ 40Â teams is selected at random from the population, select the expected mean and standard deviationÂ of the sampling distribution below.

• ÏƒxÂ¯=\$185
• ÏƒxÂ¯=\$29.25
• ÏƒxÂ¯=\$4.63
• Î¼xÂ¯=\$118.59
• Î¼xÂ¯=\$18.75
• Î¼xÂ¯=\$750

Question

A statistics student is trying to decide whether she should take a gamble and play Bingo.Â The average Bingo player earnsÂ \$9Â per game, distributed normally, with a population standard deviation ofÂ \$8. If a sample ofÂ 25Â Bingo players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.

The standard deviation of the sampling distribution is:

ÏƒxÂ¯=Ïƒnâˆ’âˆ’âˆš=\$825âˆ’âˆ’âˆš=\$1.60

Question

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

Question

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

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

Question

The average time it takes a certain brand of ibuprofen to start working isÂ 25Â minutes, with a standard deviation ofÂ 13Â minutes, distributed normally.Â A pharmacist randomly samplesÂ 20Â pills from this brand, because she isÂ 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:

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