# Thread: Need help with bernoulli trails

1. ## Need help with bernoulli trails

A recent national study showed that approximately 45% of college students binge drink. Let X equal the number of students
in a random sample of size n = 12 who binge drink. Find the probability that
(a) X is at most 5
(b) X is at least 6
(c) X is equal to 7
(d) Give the mean, variance, and standard deviation of X

I tried solving the answers and received the following
(a) 0.5269
(b) 0.96615
(c) 0.148945
(d) mean = 0.45, variance = 0.2475, standard deviation = 0.4975

2. Originally Posted by MathRules!
A recent national study showed that approximately 45% of college students binge drink. Let X equal the number of students
in a random sample of size n = 12 who binge drink. Find the probability that
(a) X is at most 5
(b) X is at least 6
(c) X is equal to 7
(d) Give the mean, variance, and standard deviation of X

I tried solving the answers and received the following
(a) 0.5269
(b) 0.96615
(c) 0.148945
(d) mean = 0.45, variance = 0.2475, standard deviation = 0.4975
The following answers are wrong:

(b) Try again.
(d) All of it. eg. Mean = np .... how can you get 0.45 from this?

3. Originally Posted by MathRules!
A recent national study showed that approximately 45% of college students binge drink. Let X equal the number of students
in a random sample of size n = 12 who binge drink. Find the probability that
(a) X is at most 5
(b) X is at least 6
(c) X is equal to 7
(d) Give the mean, variance, and standard deviation of X

I tried solving the answers and received the following
(a) 0.5269
(b) 0.96615
(c) 0.148945
(d) mean = 0.45, variance = 0.2475, standard deviation = 0.4975

Originally Posted by mr fantastic
The following answers are wrong:

(b) Try again.
(d) All of it. eg. Mean = np .... how can you get 0.45 from this?

Ok, I see my error in d
(d) So for the mean = np, therefore 12(.45) = 5.4
variance = np(1-p) = 5.4 (1-.45) = 2.97
standard deviation = sqrt(2.97) = 1.72

for b I am still working on it. I still don't see my error.

4. I think I found the answer to part b.

b) so when X is at least 6: 1 - P(X >=5) = 1- 0.5269 = 0.4731

5. Originally Posted by MathRules!
I think I found the answer to part b.

b) so when X is at least 6: 1 - P(X >=5) = 1- 0.5269 = 0.4731
I think you meant to post $\displaystyle 1 - \Pr(X {\color{red}\leq} 5)$ since your answer is correct.