Answer:
The probability that the sample proportion will be less than 0.05 is 0.80511.
Step-by-step explanation:
We are given that a courier service company wishes to estimate the proportion of people in various states that will use its services.
Suppose the true proportion is 0.04 and 349 are sampled.
<u><em>Let </em></u><u><em> = sample proportion</em></u>
The z score probability distribution for sample proportion is given by;
Z = ~ N(0,1)
where, = sample proportion
n = sample size = 349
p = population proportion = 0.04
Now, the probability that the sample proportion will be less than 0.05 is given by = P( < 0.05)
P( < 0.05) = P(
<
) = P(Z < 0.86) = 0.80511
<em>The above probability is calculated by looking at the value of x = 0.86 from the z table which has an area of 0.80511.</em>
Hence, the probability that the sample proportion will be less than 0.05 is 0.80511.