A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.06.
If 367 are sampled, what is the probability that the sample proportion will be less than 0.08? Round your answer to four decimal places.
Solution
Given that,
p = 0.06
1 - p = 1 - 0.06 = 0.94
n = 367
_{} = p = 0.06
_{} = [p ( 1 - p ) / n] = [(0.06 (0.94)) / 367 ] = 0.0124
P( < 0.08)
= P[( - _{} ) / _{} < (0.08 - 0.06) / 0.0124]
= P(z < 1.61)
= 0.9463
Probability = 0.9463
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