Question

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with a mean of 266 days and a standard deviation of 16 days.

a) What is the median pregnancy length?

b) What is the interquartile range for this distribution?

Answer 1

a.
The mean, median and mode of normal distribution are equal (because of symmetric nature). So median is 266
b.
First Quartile separates the first 25% of the data from the rest 75%.
Second Quartile separated the first 75% of the data from the rest 25%.
So for first quartile, we look for the value closest to 0.25 in standard normal table and read it's corresponding z-score which is -0.67
For third quartile , we look for the value closest to 0.75 in standard normal table and read it's corresponding z-score which is +0.67
IQR is computed by subtracting the first quartile from the third quartile. In a standard normal distribution (mean 0 and standard deviation 1), the first and third quartiles are located at -0.67 and +0.67 respectively. Thus the interquartile range (IQR) is 1.34
In any normal distribution: IQR = Q₃ - Q₁ = 0.67σ - (-0.67σ) = 1.34σ
σ = 16
IQR = 1.34 x 16 = 21.44