Question

Assume that 500 invitations have been sent out for a given event. Assume that
each person shows up independently of the others with probability 0.6.
(a) What is the probability that 250 or less people show up?
(b) Find b so that the number of people that show up is b or larger with
probability 0.9.

Answer 1

n = 500

p = 0.6

q = 1-p = 0.4

Mean = np

= 500x0.6

= 300

Standard deviation =

= 10.95

P(X < A) = P(Z < (A - meaan)/standard deviation)

a) P(250 or less people showing up) = P(X < 250.5) (continuity correction of 0.5 applied)

= P(Z < (250.5 - 300)/10.95)

= P(Z < -4.52)

= 0

b) P(X b) = 0.9

P(X < b) = 1 - 0.9 = 0.1

P(Z < (b - 300)/10.95) = 0.1

From standard normal distribution table, take Z value corresponding to 0.1

(b - 300)/10.95 = -1.28

b = 286