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. If 349 are sampled, what is the probability that the sample proportion will be less than 0.05

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.

Let = sample proportion

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

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.

Hence, the probability that the sample proportion will be less than 0.05 is 0.80511.

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!