Help! Troubleshooting a Technical Problem

[gtfitzpatrick]

Hi,
Trying to figure this out any ideas as to what I am doing wrong?
Thanks all

 

[RPinPA]

You are using the expressions for "exactly 40 occurrences" and "exactly 30 occurrences". So when you did $1 - P(40)$ you've calculated the probability of "anything but 40".

The first question asks for "at least 40". That means 40, or 41, or 42, or ... up to 100. The probability of that would be P(40) + P(41) + P(42) + ... + P(100). Or 1 minus P(0) + P(1) + ... + P(39). Either way, it would be a lot of calculation to add up all those terms. So you're probably expected to use the normal approximation to the binomial distribution.

Does that ring a bell as something you were recently taught in class?

Similarly, part (ii) asks for "at most 30". That means 30, or 29, or 28, or... down to 0. Again, easier with the normal approximation.

 

[gtfitzpatrick]

Hi,
Thanks a million for the response.
Do I not need the mean and the standard deviation, To calculate the z scores? Using the information i have is the only way can do by adding them all up?

 

[RPinPA]

Hi,
Thanks a million for the response.
Do I not need the mean and the standard deviation, To calculate the z scores

Yes. You have $n = 100$ Bernoulli trials, and the probability of "success" on each one is $p$, which you know. You are interested in the distribution of the number of successes. That is a binomial random variable. Its mean and standard deviation are formulas in terms of $n$ and $p$.

Hi,
Using the information i have is the only way can do by adding them all up?

Or by approximating as a normal random variable with the same mean and standard deviation.

Consult your textbook for "mean of a binomial distribution" and "standard deviation of a binomial distribution".