Question
Asked Nov 16, 2019
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The amount of coffee that people drink per day is normally distributed with a mean of 16 ounces and a standard deviation of 4 ounces. 18 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.

  1. For the 18 people, find the probability that the average coffee consumption is between 15 and 17.5 ounces of coffee per day. 
  2. For part d), is the assumption that the distribution is normal necessary? NoYes

 

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Expert Answer

Step 1

Solution: We are given that the amount of coffee that people drink per day is normally distributed with a mean of 16 ounces and a standard deviation of 4 ounces.

 

Step 2

We are required to find the the average coffee consumption is between 15 and 17.5 ounces of coffee per day.

 

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P(5 x17.5)

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Step 3

Using the z-score formula, w...

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17.5-16 15-16 P(15<x17.5) P 4 4 18 18 - P(-1.0607 z<1.5910) Now using the standard normal table, we have P(15 <x<17.5) P(z<1.5910)-P(z<-1.0607) -0.9442-0.1444 = 0.7998

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