Question

A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.03. If 476 are sampled, what is the probability that the sample proportion will be less than 0.04

Answer 1

The probability that the sample proportion will be less than 0.04 is 0.8995 or 89.95%.

The true proportion (p) is given to be 0.03.

Therefore, Mean (μ) = p = 0.03.

The standard error of sampling distribution can be calculated using the formula σ = √[{p(1 - p)}/n], where n, is the sample size, that is, n = 476.

Therefore, σ = √[{0.03(1 - 0. 03)}/476] = 0.00782.

Since, np = 14.28 and n(1 - p) = 461.72 are both greater than 5, we assume the sample is normally distributed.

Since, we are asked to find the probability that the sample proportion is less than 0.04, we using our calculator, enter as following:

Normalcdf(-100000000,0.04,0.03,0.00782), which gives us the value 0.8995 or 89.95%.

Thus, the probability that the sample proportion will be less than 0.04 is 0.8995 or 89.95%.

Learn more about probability of sampling distributions at

brainly.com/question/15520013

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