Question

Ten percent of graduating college seniors report planning to spend at least one year volunteering for a charitable organization. You interview 30 randomly selected graduating seniors.

1. Assuming that all the binomial conditions are met, determine the probability that exactly one student in this group of 30 plans to volunteer.

a. .2234-

b. .1775

c. .1612

d. .1413

e. .2972

2. Assuming that all the binomial conditions are met, determine the probability that at least three students in the group plan to volunteer.

a. .4889 -

b. .5886

c. .6214

d. ,6652

e. .4116

3. Assuming that all the binomial conditions are met, determine the probability that no more than 4 students in the group plan to volunteer.

a. .7663

b. .8598

c. .8246

d. .8916

e. .9113

4. Assuming that all the binomial conditions are met, determine the probability that between 2 and 5 students in the group plan to volunteer.

a. .5219

b. .7432

c. .7873

d. .8226

e. .6482

Answer 1

The population proportion of success is p = 0.1, also, 1 - p = 1 - 0.1 = 0.9, and the sample size is n= 30. We need to compute

= 0.1413

= 0.0424 + 0.1413 + 0.2277

= 0.4114

= 1 - 0.4414

= 0.5886

Pr(X <= 4)=Pr(X=0)+Pr(X=1)+Pr(X=2)+Pr(X=3)+Pr(X=4)

Pr(X <= 4)= 0.0424 + 0.1413 + 0.2277 + 0.2361 + 0.1771

Pr(X <= 4) =0.8246

Pr(2≤X≤5)=Pr(X=2)+Pr(X=3)+Pr(X=4)+Pr(X=5)

Pr(2≤X≤5) = 0.2277 + 0.2361 + 0.1771 + 0.1023

Pr(2≤X≤5) =0.7432