Question

The amount of time fathers spend with their child(ren) follows a normal distribution with mean 7 hours and standard deviation 0.5 hours. Determine the sampling distribution of the sample mean for samples of size n = 4. Indicate the mean (round to two decimal places), standard deviation (round to two decimal places), and shape (normal or not normal).
The mean of the sample mean is ______ hours; the standard deviation of the sample mean is _______ hours; and the shape of the sample mean is _________.

Answer 1

Solution :

Given that,

The sampling distribution of mean is ,

= 7

The sampling distribution of standard deviation is ,  

= / n = 0.5 / 4 = 0.25

The mean of the sample mean is 7 hours; the standard deviation of the sample mean is 0.25

hours; and the shape of the sample mean is normal .