Question

Assume that 35% of all patients in ER have COVID. Consider a random sample of 90 patients and let X denote the number among these that have COVID.

If only 5% (rather than 35%) of patients have COVID, does the normal approximation still hold? Build a pmf table, create histograms?

Answer 1

The normal distribution can be used as an approximation to the binomial distribution, under certain circumstances, namely: If X ~ B(n, p) and if n is large and/or p is close to ½, then X is approximately N(np, npq).

The Approximation to Be Accurate if Np > 5 And Nq > 5.

Here ,

n * p = 90 * 0.05 = 4.5 < 5

Therefore, we can't use normal approximation for p = 5% .

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