Need help/clarification-confused-binomal probability

[meiko]

I am at a complete loss on this problem, I would appreciate any help at all.

A marketing firm found that 49% of people don't think that having a college education is important to succeed in the business world. If a random sample of seven people is selected, find the probability that at least four people will agree with that statement. Round to 3 decimal places.

Note: the ^ is for the exponent, so ^4 is the exponent of 4

I have P(x=4), with the formula of 7C4 (0.49)^4 (0.51)^3
so (35) ( .0576) (.1327)
= 2.016 x's .1327= .2675

the book says that the correct answer is .478

What am I doing wrong...with this. I have spent way too much time on this already and I have emailed my teacher and she gives me the answer of .2676 which makes me even more confused because the correct answer according to the book is .478 - I've been banging my head against the wall going around in circles.

Thanks in advance

 

[JeffM]

I am at a complete loss on this problem, I would appreciate any help at all.

A marketing firm found that 49% of people don't think that having a college education is important to succeed in the business world. If a random sample of seven people is selected, find the probability that at least four people will agree with that statement. Round to 3 decimal places.

Note: the ^ is for the exponent, so ^4 is the exponent of 4

I have P(x=4), with the formula of 7C4 (0.49)^4 (0.51)^3
so (35) ( .0576) (.1327)
= 2.016 x's .1327= .2675

the book says that the correct answer is .478

What am I doing wrong...with this. I have spent way too much time on this already and I have emailed my teacher and she gives me the answer of .2676 which makes me even more confused because the correct answer according to the book is .478 - I've been banging my head against the wall going around in circles.

Thanks in advance

Here is, I think, where you are stuck:

The problem says "at least 4". So is 4 the only result the probability of which is relevant? Do you think 5 is at least 4? Maybe there are other results to be considered if you think that both 4 and 5 satisify the conditions of the problem.

You will see a lot of problems on tests that say "at least" x or "at most" x. You have the tools to do this. You just did not read the problem carefully enough.

PS I have done the computations myself. Your teacher gave you an answer that is relevant to the problem at hand. The book gave you an answer that is relevant to the problem at hand. However, as I am sure you have guessed by now, only one of the answers is the answer to the precise problem at hand.