Question

60% of all 3 to 5 year old children in the United States are enrolled in preschool. If a sample of 12 children is randomly selected, find the following probabilities.

a. what is the probability at least 8 children are enrolled in preschool?

Answer 1

Probability that a 3 to 5 year old child in US is enrolled in preschool is = 60% = 0.6.

We need to find that out of 12 randomly picked students atleast 8 children are enrolled in preschool=

This is a case of binomial distribution.

In binomial distribution,

P(X=x) = nCx * px * (1-p)(n-x),

where n is the total number of observations

x = Total number of favourable outcomes required

p = Probability of the favourable outcome.

In this case, we need to find P(X > = 8).

So the equation would be =

P(X = 8) + P(X=9) + P(X=10) + P(X=11) + P(X=12)

= 12C8 * 0.68*0.44 + 12C9 * 0.69*0.43

+12C10 * 0.610*0.42 +12C11 * 0.611*0.41+

+ 12C12* 0.612 * 0.40

= 0.2128 + 0.1419 + 0.0639 + 0.0174 + 0.0022

= 0.4382.

So the probability that out of 12 randomly picked students, atleast 8 will be enrolled in preschool is 0.4382.

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