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.

Question

Carl Swisher · Accepted Answer

Given number of rolls of the die are n=1000. Let the event of six coming up be succes. Then, in each trial, the probability of success is  p=P[≻ess]=P[6]=16  Let X be the random variable for the number of sixes in the 1000 rolls of the die. Then,  X∼B∈(1000,16)  Since, n is very large, the binomial random variable can be approximated as nominal random variable with mean μ=np=1000×16=166.67 and variance σ2=np(1−p)=1000×16×56=138.85. Thus  X∼N(166.67,138.85)  Now, [150≤X≤200=P[150−166.6711.78≤X−μσ≤200−166.6711.78]  =P[Z&amp;lt;−0.928]  =Φ(−0.928)  =0.1767

One thousand independent rolls of a fair die will be

Answered question

Answer & Explanation

New Questions in Other