The probability that any one student at a particular school of 784 students has an iPad is 0.124. The probability, rounded to the nearest hundredth, that more than 100 students in the school have an iPad is _____.
This is one question out of a massive booklet, and for some reason this one is giving us issues. The answer in the key is 0.36, however we must show the work.
How must we go about this?
Thank you in advance
This is one question out of a massive booklet, and for some reason this one is giving us issues. The answer in the key is 0.36, however we must show the work.
How must we go about this?
Thank you in advance
-
Jonathan -
This is Binomial with n = 784 and p = 0.124.
P( X > 100) = 0.356562 (TI-84 calculator)
Now, as you know, this would be a treacherous calculation with 684 binomial terms.
Instead, you could approximate it using the Normal ...
mean = np = 97.216
std. dev. = sqrt[np(1-p)] = 9.2283
Using the "continuity adjustment" ...
P(X > 100) = P[z > (100.5 - 97.216) / 9.2283] = P(z > 0.356) = 0.3609
Hope that helps
This is Binomial with n = 784 and p = 0.124.
P( X > 100) = 0.356562 (TI-84 calculator)
Now, as you know, this would be a treacherous calculation with 684 binomial terms.
Instead, you could approximate it using the Normal ...
mean = np = 97.216
std. dev. = sqrt[np(1-p)] = 9.2283
Using the "continuity adjustment" ...
P(X > 100) = P[z > (100.5 - 97.216) / 9.2283] = P(z > 0.356) = 0.3609
Hope that helps