Suppose 46% of american singers are grammy award winners.
if a random sample of size 622 is selected, what is the probability that the proportion of grammy award winners will be less than 47%? round your answer to four decimal places.

The probability that the proportion of Grammy award winners will be less than 47% is 0.6915

Step-by-step explanation:

* Lets explain how to solve the problem

- Suppose 46% of American singers are Grammy award winners.

- In a random sample of size 622 is selected

- We want to find the probability that the proportion of Grammy award

 winners will be less than 47%

* At first we must to calculate z

∵ , where

# P' is the sample proportion

# n is the sample size

# P is probability of success

∵ The sample proportion is 47% = 47/100 = 0.47

∴ P' = 0.47

∵ The sample size is 622

∴ n = 622

∵ The probability of success is 46% = 46/100 = 0.46

∴ P = 0.46

∴

- P(P' < 0.47) = P(z < 0.5004)

∵ P(z < 0.5004) = 0.6915

∴ P(P' < 0.47) = 0.6915

* The probability that the proportion of Grammy award winners will

 be less than 47% is 0.6915