Question

1. Three random people get on a bus. Assume that boys and girls are equally likely to get on the bus. Let x represent the number of girls that get on the bus. Construct a probability distribution.

2. Find the value of z to the left of the mean so that 71.55% of the area under the distribution curve lies to the right of it.

3. According to a study done by a research center, 39% of adults believe that courting is now obsolete.

A) What is the probability that in a random sample of 300 adults less than 38% believe that courting is obsolete?

B) What is the probability that in a random sample of 300 adults between 30% and 35% believe courting is obsolete?

Answer 1

(1)

x	P(x) = C(3, x) 0.5^x 0.5^(3 - x)
0	0.125
1	0.375
2	0.375
3	0.125

(2)

z- score such that 71.55% (0.7155) area lies to its right is z = -0.5695

(3)

p = 0.39, n = 300

SE = √{p(1 - p)/n} = √{0.39(1 - 0.39)/300} = 0.0282

(A) z = (p' - p)/SE = (0.38 - 0.39)/0.0282 = -0.3551

P(p' < 0.38) = P(z < -0.3551) = 0.3613

(B) z1 = (0.3 - 0.39)/0.0282 = -3.196 and z2 = (0.35 - 0.39)/0.0282 = -1.4204

P(0.3 < p' < 0.35) = P(-3.196 < z < -1.4204) = 0.077