Suppose a large consignment of cell phones contained 19% defectives. If a sample of size 399 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 5%? Round your answer to four decimal places.
Solution
Given that,
=
[p
( 1 - p ) / n] =
[(0.19 * 0.81) / 399] = 0.0196
= P[ -0.05 / 0.0196 < (
-
) /
< 0.05 / 0.0196]
= P(-2.55 < z < 2.55)
= P(z < 2.55) - P(z < -2.55)
= 0.9892
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