Question

1. A study released by the governor’s office stated that 60% of the state residents support a higher penalty for driving under influence. John thinks the number is low, so he decided to conduct his own survey. He interviews 100 people and find that 75% support a higher penalty for driving under influence. Identify the following: (1pt each)

- Sample:

- Population:

- Statistic:

- Parameter:

2. A bag contains 5 colored marbles, 3 red and 2 blue. You want to pick three marbles, one at a time from the bag. The sample space of this experiment is as followed:

S = {RRR, RRB, RBR, BRR, BBR, BRB, RBB}

We define the following event:

A – No pick is red

B – Exactly two picks are Red.

C – The second is Blue.

D – Exactly two Blue.

a. Is A and B disjoint or non-disjoint? (2pts)

b. Is C and D disjoint or non-disjoint? (2pts)

3. A carnival game has bag that contains four different colored balls. There are four blue balls, three red balls, two orange balls, and one purple ball. You pay $5 to reach in and grab one colored ball from the bag. If you pick a blue ball you win $10, if you pick a red ball you win $20, if you pick an orange ball you win $50, and if you pick a purple ball you win $100. What is your expected gain if you play this game? (3pts)

Answer 1

1.

Sample

Those 100 people who were interviewed by John constitutes the sample here.

Population

Residents of that particular state constitutes the population here.

Statistic

Statistic is some value obtained from observer's sample. The proportion obtained from sample is the statistic.

Parameter

Parameter is some value obtained about the population. The proportion corresponding to the population is parameter here.

2.

(a)

So, A and B are disjoint.

(b)

So, C and D are non-disjoint.

3.

Suppose, random variable X denotes gain (after subtracting payment to reach in from winnings) in dollars.

So, expected gain is $ 25.