Question

The Department of Education in a certain state wishes to establish a state-subsidized school lunch program. It claims that 40% of all elementary school children in the state are now inadequately nourished. In a sample of 150 elementary school children from this state, what is the probability that at least 50 are inadequately nourished, if the Department of Education’s claim is valid?

Answer 1

let

X be random variable of number of elementary School children are inadequantely nourished

X~B(n ,p)

here n=150

p= 0.4

as n =150 and p =.4 so we can used

normal approximation

as n is large

X~N( np, npq) -----------------------as np>5

X~N( 60 ,36)

Now

probability that at least 50 school children  are inadequantely nourished

P(X>50)= P(X > 50.5) -------------------as we are converting descrete random variable to continuous.

-----------------------------by symmetric property of normal distribution

---------------------------------------- ans

probability that at least 50 school children  are inadequantely nourished is 0.94295