Question

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.

Answer 1

Given data

total grammy award winners =465

Population Propertion of sucess

Population Propertion of failure

number of sample taken (n)=622

sample proportion of sucess

Now we have to find the probablity for a propertion within the is less than 47%

Now lets calculate Z score for this situation first ,so

Now from the Standard probablity table of Z score the probablity value for Z=0.50 is

P=0.6915

As we look into the bell shape curve for this Z score we find that this P=0.6915 is the probablity below thw point Z=0.50 .Hence it is the required probablity .

So the probablity that the proportion of grammy award winner will be less than 47% in the sample of 622 is P =0 .6915