Question

Two percent of hairdryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, exactly 225 are defective. (Hint: use the normal distribution as an approximation to the binomial distribution).

Answer 1

This is a binomial distribution question with

n = 10000

p = 0.02

q = 1 - p = 0.98

This binomial distribution can be approximated as Normal distribution since

np > 5 and nq > 5

Since we know that

P(X = 225.0) = ?

For a continuous, the probability is the integration of probability density function in a given interval. Since if we give a particular point as an interval the integration comes out as 0.

P(X = 225.0) = 0

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