Question

An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via​ "smart phones", so they want to estimate the proportion of users who access the site that way​ (even if they also use their computers​ sometimes). They draw a random sample of

200200

investors from their customers. Suppose that the true proportion of smart phone users is

3737​%.

​a) What would the standard deviation of the sampling distribution of the proportion of the smart phone users​ be?

. 034.034

​(Round to three decimal places as​ needed.)​b) What is the probability that the sample proportion of smart phone users is greater than

0.370.37​?

. 5.5

​(Round to three decimal places as​ needed.)​c) What is the probability that the sample proportion is between

0.320.32

and

0.420.42​?

nothing

​(Round to three decimal places as​ needed.)

Answer 1

Solution:

Given:

The true proportion of smart phone users = 37% = 0.37

That is: p = 0.37

Sample Size = n = 200

Part a)  What would the standard deviation of the sampling distribution of the proportion of the smart phone users​ be?

Part b) What is the probability that the sample proportion of smart phone users is greater than 0.37?

That is:

Find z score :

where

Thus

Thus we get:

Look in z table for z = 0.0 and 0.00 and find area.

Thus P( Z< 0.00) = 0.5000

Thus

Part c) What is the probability that the sample proportion is between 0.32 and 0.42​?

Thus find z score:

and

Thus we get:

Look in z table for z = 1.4 and 0.07 as well as for z = -1.4 and 0.07

and find area.

P( Z < 1.47 ) = 0.9292

P( Z < -1.47) = 0.0708

Thus