Suppose that asthma affects 1 in 20 children in a population. You take a simple

Question

Suppose that asthma affects 1 in 20 children in a population. You take a simple random sample of 300 children from this population.

What is the probability of seeing at least 25 cases in a sample? Hint: Use the Normal approximation to the binomial

Show all your steps/work for full points. Carry probabilities to at least 4 decimal places for intermediate steps. Round your final answer to two or three decimal places. For extremely small probabilities, it is important to have 1 or two significant digits (non-zero digits), such as 0.000001 or 0.000034, etc.

Explanation / Answer

here p=1/20=0.05

therefore mean =np=300*0.05=15

and std deviation =3.7749

hence probability of seeing at least 25 cases in a sample =P(X>=25)=1-P(X<=24)

=1-P(Z<(24.5-15)/3.7749)=1-P(Z<2.5166)=1-0.9941=0.0059

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