In: Statistics and Probability
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?
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