Question

A fair die is rolled 300 times and each time a number evenly divisble by three is​ rolled, a success is recorded. Find the probability of obtaining the​ following: Between 90 and 110 successes​ (inclusive) ​(Round to four decimal ​places)

Answer 1

P(success) = P(number divisible by 3), p = 1/3

q = 1 - 1/3 = 2/3

Number of trials, n = 300

Normal approximation to binomial: P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = np

= 300 x 1/3

= 100

Standard deviation =

=

= 8.165

P(between 90 and 110 successes​, inclusive) = P(90 X 110)

= P(X < 110.5) - P(X < 89.5)

= P(Z < (110.5 - 100)/8.165) - P(Z < (89.5 - 100)/8.165)

= P(Z < 1.29) - P(Z < -1.29)

= 0.9015 - 0.0985

= 0.8030