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 200 investors from their customers. Suppose that the true proportion of smart phone users is 43%.a) What would the standard deviation of the sampling distribution of the proportion of the smart phone users be?

a)

b)

c)

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

X represent the users who access the site on the way specified

estimation for the sample proportion

n=200 sample size selected

We are interested in the distribution for the true proportion.  

The population proportion have the following distribution  

And the reason is because the sample size is large enough and the estimated proportion is near to 0.5

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

For this case we know that the expected value would be:

And for the standard deviation we have:

And if we replace we got:

What is the probability that the sample proportion of smart phone users is greater than  0.33?

For this case we can use the z score formula given by:

And we want this probability:

If we use the z score we got:

c) What is the probability that the sample proportion is between 0.19 and 0.31?

We can use the z score formula and we have: