The CDC reported that 1 in 88 American children had been dia

The CDC reported that 1 in 88 American children had been diagnosed with an autism spectrum disorder (ASD).

a) If a random sample of 200 American children is selected, what are the expected value and standard deviation or the number who have been diagnosed with ASD?

b) Calculate the approximate probability that at least 2 children in the sample have been diagnosed with ASD?

c) If the sample size is 352, what is the approximate probability that fewer than 5 of the selected children have been diagnosed with ASD?

Solution

p=1/88

a) n=200, we use poisson distirbution here since n is large and p is small

lamda=1/88*200=2.2727=mean

sd=sqrt(lamda)=1.50755

b) P(x>=2)=1-P(x<2)

use POISSON.DIST function in excel

P(X>=2)=1-0.3371=0.6628

c) n=352

lamda=352*(1/88)=4

P(X<=5)

P(x<=5)=0.78513