Question

In: Statistics and Probability

b. Calculate the probability that 31​% or more of the sample will be living in poverty....

b. Calculate the probability that 31​% or more of the sample will be living in poverty. Assume the sample is collected in such a way that the conditions for using the CLT are met. Upper P left parenthesis Modifying Above p with caret greater than or equals 0.31 right parenthesis equals nothing ​(Round to three decimal places as​ needed.)

Solutions

Expert Solution

Solution:

Given ,

p = 0.31 (population proportion)

Let n be the sample size,

Let be the sample proportion.

The sampling distribution of is approximately normal with

mean = =  p = 0.31

SD =   =     

Find P( > 0.31)

Observe that 0.321 is mean of the distribution of .

Since this distribution is normal , it is symmetric about its mean,

Area to left of mean = Area to the right of mean = 1/2 i,e 0.500

So ,

P( > 0.31) = 0.500

orchestra answered 3 years ago
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