Discuss the following in detail:
Q1. Suppose a single die is rolled once. You win $5 if a 1 or a 3 comes up, win $12 if a 5 comes up and lose $10 if a 2, 4, or 6 come up.
a) Complete the table that gives the expected values of each event occurring.
Event x (random variable) P(x) xP(x)
Rolling a 1 +5
Rolling a 2 -10
Rolling a 3 +5
Rolling a 4 -10
Rolling a 5 +12
Rolling a 6 -10
b) Use your table to find the expected value of the game.
c) What does the expected value tell you about the game?
Q2. Use the below problem to answer the following questions:
A farmer plants 12 saplings. On average, 15% of saplings planted fail to survive (die) their first winter.
a) What type of probability distribution is presented?
b) Find the probability that exactly 5 of his saplings will die in that first winter. Round to 4 decimal places.
c) Find the probability that 5 or less of saplings will die in that first winter. Round to 4 decimal places.
d) Find the probability that more than 5 of saplings will die in that first winter. Round to 4 decimal places.
Q3. Use the following information to answer the problems below:
Ten percent of American adults are left-handed. Suppose we have a sample of 25 people. Assume that each person in the sample is either left or right-handed.
a) Find the mean and standard deviation for the number of left-handed people in the sample.
b) Would it be unusual to survey a group of 25 people and find that 7 of them are left-handed? Explain.