One thousand independent rolls of a fair die will be made. Compute an approximation to...
One thousand independent rolls of a fair die will be made. Compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively. If the number 6 appears exactly 200 times, find the probability that the number 5 will appear less than 150 times.
Answer & Explanation
Given number of rolls of the die are . Let the event of six coming up be succes. Then, in each trial, the probability of success is
Let X be the random variable for the number of sixes in the 1000 rolls of the die. Then,
Since, n is very large, the binomial random variable can be approximated as nominal random variable with mean and variance . Thus