Statistics
posted by Patrick .
Calculate each binomial probability:
a. Fewer than 4 successes in 12 trials with a 10 percent chance of success.
b. At least 3 successes in 7 trials with a 40 percent chance of success.
c. At most 9 successes in 14 trials with a 60 percent chance of success.
d. More than 10 successes in 16 trials with an 80 percent chance of success.

If you are asked to do this by hand, try the binomial probability formula:
P(x) = nCx * p^x * q^(nx)
Note: * means to multiply; ^ means raised to the power of.
For a), use:
x = 0, 1, 2, 3
n = 12
p = .10
q = 1  p = .90
I'll let you substitute the values and take it from here. (Hint: you will have to determine P(0), P(1), P(2), and P(3), then add together for your total probability.
An easier way to do these problems is to use a binomial probability table. If you do this, you will still need to find P(0), P(1), P(2), and P(3). In the table, n = 12, p = .10, x = 0, 1, 2, 3 (for each one). Add all these probabilities together for the total probability.
I've given you some ideas using part a) as an example. I'll let you try to figure out the rest on your own. 
0.0213

.849
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