Question

The amount of coffee that people drink per day is normally distributed with a mean of 17 ounces and a standard deviation of 7 ounces. 34 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ N(___,___)
2. What is the distribution of ¯x? ¯x ~ N(___,___)
3. What is the probability that one randomly selected person drinks between 16.5 and 17.3 ounces of coffee per day?
4. For the 34 people, find the probability that the average coffee consumption is between 16.5 and 17.3 ounces of coffee per day.
5. For part d), is the assumption that the distribution is normal necessary? No or Yes
6. Find the IQR for the average of 34 coffee drinkers.
   Q1 = ___ ounces
   Q3 = ___ ounces
   IQR: ___ ounces

Answer 1

Dear student we can provide you with the solution of 4 sub question at a time.

a)distribution of X is normal with mean of 17 ounces and a standard deviation of 7 ounces

b) sample size n = 34

Standard error =

distribution of is normal with mean of 17 ounces & a standard error of 1.2

c) the probability that one randomly selected person drinks between 16.5 and 17.3 ounces of coffee per day is

( using excel formula NORM.S.DIST(0.043,TRUE)-NORM.S.DIST(-0.071,TRUE) )

d) For 34 people, the probability that the average coffee consumption is between 16.5 and 17.3 ounces of coffee per day =

( using excel formula NORM.S.DIST(0.25,TRUE)-NORM.S.DIST(-0.417,TRUE))

e) No, it is necessary as the sample size is large greater than 30, hence the centrallimit theorem applies.