Question

A die is rolled 360 times. Let say that you want to use normal approximation to find the probability that the number of 4 was rolled less than 100 times. You need to find the probability that X<100. Explain how you would use continuity correction in this case.

Answer 1

A die is rolled 360 times. Let say that you want to use normal approximation to find the probability that the number of 4 was rolled less than 100 times. You need to find the probability that X<100. Explain how you would use continuity correction in this case.

p=P( number 4) = 1/6

n=360

mean = n*p= 360*1/6 =60

standard deviation = sqrt(npq) = sqrt( 360*(1/6)*(5/6)) = 7.0711

we want to find probability that X<100, with continuity correction we have to find P( x≤ 99.5)

z value for 99.5, z = (99.5-60)/7.0711 =5.59

P( x≤ 99.5) = P( z < 5.59)

= 1.00