Quote:
a. Can you use the normal approximation to the binomial distribution to estimate
the probability that between 22 and 35 of them have faulty control panels?
Explain.
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The normal approximation is appropriate when np and n(1-p) are both large. How large depends on what textbook/lecturer you have. If you are feeling keen, calculate both the exact value and the approximation and compare them.
Quote:
b. Estimate the probability that between 22 and 35 of them (including 22 and 35)
have faulty control panels.
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If np and n(1-p) are large,
,
Where Y has distribution N(np, np(1-p))