Question

The lengths of adult males' hands are normally distributed with mean 190 mm and standard deviation is 7 mm. Suppose that 48 individuals are randomly chosen. Round all answers to 4 where possible.

1. For the group of 48, find the probability that the average hand length is less than 192.
2. Find the third quartile for the average adult male hand length for this sample size.
3. For part b), is the assumption that the distribution is normal necessary?

Answer 1

a)

Let X denote the length of adult males' hands (in mm).

Using Central Limit theorem, we know,

Required probability =

b)

Let want to find 'x' such that

c)

No, the assumption that the distribution is normal is not necessary because irrespective of the parent population, the distribution of sample mean tends to Normal for large sample size.