Question

The Centers for Disease Control and Prevention reported in 2012 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 of the number who have been diagnosed with ASD?

b. Referring back to (a), 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?

Answer 1

P = 1/88

n=200

Mean, λ = ( 1/18) * 200

= 2.2727

std dev = √λ =    1.50755

.........

poisson probability distribution

P(X=x) = e-λλx/x!

X	P(X)
0	0.1030
1	0.2342

p(atleast 2) = p(x>=2) = 1- p(x<2)

= 1 -(p(0) + p(1))

= 1-0.1030-0.2342

=0.66281

..............

n=352

Mean λ = 1/88*352 = 4

X	P(X)
0	0.0183
1	0.0733
2	0.1465
3	0.1954
4	0.1954

p(fewer than 5 ) = p(x<5) = p(0)+p(1)+p(2)+p(3)+p(4)

so,

p(X<5) = 0.6288

revert back for doubt

thumbs up please