According to one study, brain weights of men are normally distributed with a mean of 1.20kg and a standard deviation of 0.13kg. Use the data to answer questions (a) through (e).
a. Determine the sampling distribution of the sample mean for samples of size 3.
The mean of the sample mean is μx=1.20.
The standard deviation of the sample mean is σx=0.0751.
(Round to four decimal places as needed.)
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of
1.20 kg.
(Round to two decimal places as needed.)
e. Determine the percentage of all samples of twelve men that have mean brain weights within 0.1 kg of the population mean brain weight of
1.20 kg.
(Round to two decimal places as needed.)
b. Determine the sampling distribution of the sample mean for samples of size 12.
The mean of the sample mean is μx=1.20.
The standard deviation of the sample mean is σx=0.0375.
(Round to four decimal places as needed.)
c. Construct a graph of the normal population distribution and the two sampling distributions for brain weights.