Question

Find the probability that in 200 tosses of a fair six-sided die, a three will be obtained at most 40 times.

A) 0.9147 B) 0.0853 C) 0.8810 D) 0.1190

Answer 1

Soln,

Since this is a binomial distribution with n=200 and p=1/6;
np=200/6=33.33
n(1-p)=200*5/6=166.67
both np and n(1-p) are greater than 5, so we can assume the distribution with a normal distribution

Hence = 33.33

Also

Hence standard deviation =?27.778= 5.270

So., P(x?40) = Probability of most 40 times of appearing a three

P(zThe probabilities are approximated using a continuity correction

So the probability that the number of threes less than or equal to 40 is approximately

(x-?)/?) =P(z?(40. 5-33.33)/5.27) =P(z?1.36)= 0.91~0.914(aproxx)