Question

The amount of coffee that people drink per day is normally distributed with a mean of 14 ounces and a standard deviation of 5 ounces. 32 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.

1. What is the probability that one randomly selected person drinks between 13.7 and 14.1 ounces of coffee per day?
2. 
   
3. For the 32 people, find the probability that the average coffee consumption is between 13.7 and 14.1 ounces of coffee per day.
4. 
   
5. For part b, is the assumption that the distribution is normal necessary? NoYes
6. 
   
7. Find the IQR for the average of 32 coffee drinkers. Round to two decimal places.
   Q1 =  ounces
   Q3 =  ounces
   IQR:  ounces

Answer 1

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Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(0.02, TRUE)" & "=NORM.S.DIST(-0.06, TRUE)" to find the probability.

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Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(0.1131, TRUE)" & "=NORM.S.DIST(-0.3394, TRUE)" to find the probability.

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Since the sample size is greater than 30.

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Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.25 to the left of the normal curve OR use excel formula "=NORM.S.INV(0.25)" to find the z-score.

Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.75 to the left of the normal curve OR use excel formula "=NORM.S.INV(0.75)" to find the z-score.