Probability: reviewing claims regarding college students and

This from a practice test that my teacher gave me to help review. I know the answer to 10 is B or D because...well to be honest I don't know for sure. I don know that A is wrong because there is no reason to include 2 in the answer and I'm pretty sure C is wrong because it should be .5 (to make it 50%) not 5 and I believe that 1.58 is just some random number. But when it comes down to choosing between B and D I don't know.

For 11 I know that n=10 because that's the number or trials that the management would be conducting. I also know that the answer is going to be below .5 because it has to be below the 50% of the ten students that are exspected to know about the website. Other then that I'm pretty much lost.

A popular Web site among college students is studentinfo.com. It lists information about jobs both in the United States and abroad. The management of the Web site claims that half of all college students know abut the Web site. You do not quite believe them and think it is much less than half. You decide to ask a sample of ten students if they know about the Web site. Out of the ten students asked, only two had heard of the Web site.

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10. If the management of the Web site is correct about the proportion of all college students who know about the Web site, what is the distribution of the number of students who know about the Web site in a simple random sample of ten students?
A. B(10, 2) B. B(10, 0.5) C. N(5, 1.58) D. N(10, 0.5)

11. If the management of the Web site is correct about the proportion of students who know about the Web site, what is the probability that you would find only two students who know about the Web site in a simple random sample of ten students?
A. 0.044. B. 0.055. C. 0.115. D. 0.244.

For #11, you can just use a binomial.

\(\displaystyle C(10,2)(0.5)^{2}(0.5)^{8}\)

If you perform a hypothesis test with a level of confidence of 0.01, you get a 'do not reject' the null hypothesis.

The claim is that less than half know about the web site.

\(\displaystyle H_{0}\geq{0.5}\)

\(\displaystyle H_{a}<{0.5}\)(claim)

We do not reject the null hypothesis. Therefore, there is not enough evidence to support the claim that less than half the students know about the web site. So, we would assume that management is correct afterall.
The p value is 0.0289. So, if you want to reject the null hypothesis use an alpha level of, say, 0.05