A courier service company wishes to estimate the proportion

A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.07. If 298 are sampled, what is the probability that the sample proportion will differ from the population proportion by greater than 0.03? Round your answer to four decimal places.

Solution

Answer to the question)

P = 0.7

n = 298

SE = sqrt(p*(1-p)/n)
SE = sqrt(0.7*0.3/298)

SE = 0.0265

.

x1 = 0.7-0.03 = 0.0.67

x2 = 0.7+0.03 = 0.73

.

P(p < 0.67) =

z = (0.67 -0.7) / 0.0265 = -1.13

P(z <-1.13) = 0.1292

.

P(p > 0.73) = 1 - P9p < 0.73)

z = (0.73-0.7) / 0.0265

z = 1.13

.

P(z > 1.13) = 1 - P(z < 1.13)

P(z > 1.13) = 1 - 0.8708

P(z > 1.13) = 0.1292

.

Thus probability of difference greater than 0.03 = 0.1292+0.1292 = 0.2584