A couple Stats problems

[camcurrie]

Here are a couple stats problems which I have attempted but don't seem to be getting anywhere as I believe I have done some wrong steps..

An advertising agency conducted an ad campaign aimed at mking consumers in BC aware of a new product. Upon completion of the campaign, the agency claimed that 20 percent of consumers in the province had become aware of the product.

a) the product's distributor surveyed 1,000 consumers inBC and found that only 150 were aware of the product. This causes the distributor to question the accuracy of the ad agency's claim, so the distributor would like to calculate the probability of 150 or fewer people (out of a sample of 1,000) being aware of the product if ad agency's claim is true. Why can you use the normal approximation to binomial to calculate this probability?

b) Regarding part (a), what mean and standard deviation should you use in the normal approximation?

c) Using the normal approximation, calculate the probability that 150 or fewer consumers in a random sample of 1,000 consumers would be aware of the product if the true proportion of consumers in BC that are aware of the product is 20%?


My attempts:

a) because we have n and p and from there you can standardize it and make a bell curve to find the mean and standard deviation.
b) E(X) = np = (1000)(.15) = 150
square root of (1000)(.15)(1-.15) = 11.29

I think this is completly wrong so if anyone can help that would be great.

Thanks

 

[tutor_joel]

Part A

You can use a binomial distribution here since n is large enough so as not to have a skewed distribution and it's a binomial. (binomial meaning that you have the choice of one of two outcomes...yes or no in this case)

...thinking about part b

 

[tutor_joel]

Part B

I think that the mean would be 0.2 instead of 0.15 since the claim is 0.2 and you want to find P(x \(\displaystyle \le\) 150), if the mean was 0.15, P(x \(\displaystyle \le\) 150) would be highly likely. No need to multiply by 1000 since we're only concerned about the "probability"

The standard deviation calculation I remember for binomials is

\(\displaystyle \sigma = \sqrt{p(1-p)/n}\)

You should double check your text on this one.