Question

In: Statistics and Probability

An investment website can tell what devices are used to access the site. The site managers...

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.)

Solutions

Expert Solution

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


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