Probability-binomial-distribution -1-v2 by ClassOf1

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```									              Sub: Statistics                                                                            Topic: Probability

Question:

Probability values using binomial distribution.

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Calculate each binomial probability:

(a) Fewer than 7 successes in 15 trials with a 40 percent chance of success. (Round your
answer to 4 decimal places.)

Probability

(b) At least 6 successes in 10 trials with a 70 percent chance of success. (Round your answer to
4 decimal places.)

Probability

(c) At most 12 successes in 17 trials with a 90 percent chance of success. (Round your answer
to 4 decimal places.)

Probability

(d) More than 13 successes in 19 trials with an 40 percent chance of success. (Round your
answer to 4 decimal places.)

Probability

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Sub: Statistics                                                                            Topic: Probability

Solution:

(a) Fewer than 7 successes in 15 trials with a 40 percent chance of success. (Round your
answer to 4 decimal places.)
The information can be represented in the following notation:

Sample size: n = 15 trials
Proportion: p=0.4
Here X follows Binomial distribution with parameters n = 15 and p = 0.4

The probability function of x is given by

n
P[X = x] =        * p x * q n x , x = 0, 1, 2… n; and q = 1 – 0.4 = 0.6
x

Fewer than 7 successes

X            NCx          P^x           q^(n-x)        P(X)
0         1         1           0.00047        0.00047
1        15       0.4          0.000784       0.004702
2       105      0.16          0.001306       0.021942
3       455    0.064           0.002177       0.063388
4      1365   0.0256           0.003628       0.126776
5      3003 0.01024            0.006047       0.18
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