1. Probability, Finding the Inverse Normal

2. Records indicate that the birth weights of baby boys at a particular hospital are normally distributed with standard deviation 0.4 kg.
The probability that a random baby boy weighs more than 3.2 kg is 0.10.
Find
a) the mean of the distribution
b) the expected birth weights between which 75% of all baby boys are born at the hospital.

3. Standardising P(Z > 3.2 - µ) = 0.10 0.4
Records indicate that the birth weights of baby boys at a particular hospital are normally distributed with standard deviation 0.4 kg. The probability that a random baby boy weighs more than 3.2 kg is Find a) the mean of the distribution µ
Given P(X > 3.2) = 0.10
Standardising P(Z > µ) = 0.10
0.4
Using tables µ = 1.281
Simplifying µ = 0.4 x 1.281
µ = 2.687
Rounding µ = 2.7 kg (1dp)
look up 0.40 in the body of the tables to get 1.281 µ

4. To find x P( x1 < X < x2 ) = 0.75
Records indicate that the birth weights of baby boys at a particular hospital are normally distributed with standard deviation 0.4 kg. The probability that a random baby boy weighs more than 3.2 kg is Find b ) the expected birth weights between which 75% of all baby boys are born at the hospital.
To find x P( x < X < x ) = 0.75
P(x1 – 2.7 < Z < x2 – 2.7 ) = 0.75
Using tables x1 – 2.7 = & x2 – 2.7 = 1.15
Simplifying x1 = 2.2 kg (1dp)
And x2 = 3.2 kg (1dp)
Look up in the body of the tables to get 1.15
– remember one of them has to be negative
x x2