If you roll a die 100 times, what is the approximate probability that you will roll between 11 and 14 ones, inclusive? (Round your answer to two decimal places.)

Question

You may need to use the appropriate appendix table or technology to answer this question.

If you roll a die 100 times, what is the approximate probability that you will roll between 11 and 14 ones, inclusive? (Round your answer to two decimal places.)

Answer 1

The easiest way to solve this exactly is to use Excel's binom.dist formula and find P(X <= 14) - {(X <= 10) with the probability 1/6 (the probability of getting a 1); the final 1 in the formula indicates that we have the cumulative probability rather than the probability of the value given (the probability mass function).

binom.dist(14,100,1/6,1) - binom.dist(10,100,1/6,1) = 1244725

Of course, using binom.dist, you could solve this using

binom.dist(11,100,1/6,0)+binom.dist(12,100,1/6,0)+binom.dist(13,100,1/6,0)+binom.dist(14,100,1/6,0)

Note the change from 1 to 0 in the parentheses, This would be P(11) + P(12) + P(13) + P(14)

You can solve using the binomial distribution formula P(x) = C(100,x)(1/6)^x(5/6)^(100-x) and add P(11)+P(12)+P(13)+P(14)

The final way, taught in statistics, is using a normal distribution approximation to the binomial distribution.