Question

give example of calculation of a Normal Probability.

The height of a 10-year-old girl. According to the National Center of Health Statistics, X~N(54.5, (1.24)^2 ).

The height of a 10-year-old boy. According to the National Center of Health Statistics, Y~N(54.1, (2.4)^2 ).

Find the probability that a randomly chosen 10-year-old girl will be taller than a randomly chosen 10-year-old boy.

Can you solve it using normal probability please?

Answer 1

Let X is a random variable shows the height of 10-year-old girl and Y is a random variable shows the height of 10-year-old boy. Let D = X-Y

Here D has normal distribution with mean

and standard deviation

The z-score for D = 0 is

The probability that a randomly chosen 10-year-old girl will be taller than a randomly chosen 10-year-old boy is

P(D > 0) = P(z > -0.15) = 0.5596