Question

The proportion of adult women in a certain geographical region is approximately 52 ​%. A marketing survey telephones 600 people at random. Complete parts a through c below. ​a) What proportion of the sample of 600 would you expect to be​ women? 0.52 ​(Type an integer or a decimal. Do not​ round.) ​b) What would the standard deviation of the sampling distribution​ be? SD left parenthesis ModifyingAbove p with caret right parenthesis equals0.020 ​(Round to three decimal places as​ needed.) ​c) How many​ women, on​ average, would you expect to find in a sample of that​ size? nothing women ​(Type a whole​ number.)

Answer 1

Answer :

We have given : n = 600 and p = 52 % = 0.52

## a) What proportion of the sample of 600 would you expect to be​ women?

Answer :

p = 52 / 100 = 0.52

we would expect a proportion of 0.52 of the sample to be women .

## b) What would the standard deviation of the sampling distribution​ be? SD left parenthesis Modifying Above p with caret right parenthesis equals0.020 ​(Round to three decimal places as​ needed.) ​

Answer :

p = 0.52 we know that p + q = 1

therefore q = 1 - p = 1 - 0.52 = 0.48

standard deviation = √ p*q / n

= √ ( 0.52 * 0.48) / 600 = 0.0203960 ie 0.020

= 0.020

## ​c) How many​ women, on​ average, would you expect to find in a sample of that​ size? nothing women ​(Type a whole​ number.)

Answer :

the number of women expected to an average is : n p

np = 600 * 0.52 = 312