Probability, Finding the Inverse Normal

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.

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 0.10. Find a) the mean of the distribution 0.50 0.40 0.10 µ 3.2 Given P(X > 3.2) = 0.10 Standardising P(Z > 3.2 - µ) = 0.10 0.4 Using tables 3.2 - µ = 1.281 Simplifying 3.2 - 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 0.50 0.40 0.10 µ 1.281

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 0.10. Find b ) the expected birth weights between which 75% of all baby boys are born at the hospital. To find x P( x1 < X < x2 ) = 0.75 P(x1 – 2.7 < Z < x2 – 2.7 ) = 0.75 0.4 0.4 Using tables x1 – 2.7 = -1.15 & x2 – 2.7 = 1.15 0.4 0.4 Simplifying x1 = 2.2 kg (1dp) And x2 = 3.2 kg (1dp) Look up 0.375 in the body of the tables to get 1.15 – remember one of them has to be negative 0.375 0.375 x1 2.7 x2 0.375 0.375 -1.15 2.7 1.15