Question

PLEASE do not answer if you are not sure. Second time posting. Thank you!

Let X represent a binomial random variable with n = 110 and p = 0.19. Find the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

a.	P(X ≤ 20)
b.	P(X = 10)	0.0029
c.	P(X > 30)
d.	P(X ≥ 25)

Answers I received that were not correct:

a. P ( X < 20.5 ) = 0.4602

c. P ( X > 30.5 ) = 0.0099 (WRONG)

d. P ( X > 25.5 ) = 0.1314 (WRONG)

Answer 1

Solution:- Given that n = 110, p = 0.19

Mean = n*p = 110*0.19 = 20.9

standard deviation = sqrt(npq) = sqrt(110*0.19*0.81) = 4.1145

a. P(X <= 20 ) = P(X < 20.5)

= P(Z < (20.5-20.9)/4.1145)

= P(Z < -0.0972)

= 0.4602

b. P(X = 10) = P(9.5 <= X < 10.5)

= P((9.5-20.9)/4.1145 < Z < (10.5-20.9)/4.1145))

= P(-2.7707 < Z < -2.5276)

= 0.0029

c. P(X > 30) = P(Z > (30-20.9)/4.1145)) = 0.0136

d. P(X >= 25) = P(X > 24.5) = P(Z > (24.5-20.9)/4.1145)

= P(Z > 0.8750)

= 0.1894