I have a few questions that I'm not sure how to approach, or why it's wrong (or what is the correct answer, for that matter).
Instructions: Determine whether the events are independent and give a reason.
2) The table below describes the smoking habits of a group of asthma sufferers.
Is heavy smoking independent of gender? (Choose one of the following.)
A) Yes, because each of the joint probabilities is equal to the product of the marginal probabilities.
B) No: P(male & heavy smoker) = 0.079 and P(female & heavy smoker) = 0.077. These are not equal.
C) No: overall, 15.5% of the group are heavy smokers, but 15.2% of the men are heavy smokers. These are not equal.
D) Yes: the percentage of women in each smoking category is the same as the percentage of men in each smoking category.
E) Yes: a heavy smoker cannot be both a man and a woman.
I chose option (D). I have no idea why this I got wrong. I'm assuming the answer is the opposite...? A little help?
Instructions: Find the indicated probability.
5) A tennis player makes a successful first serve 65% of the time. Assume that each serve is independent of the others. If she serves four times, what is the probability that she does not make all of her first serves? (Choose one of the following.)
A) 0.65 . . . B) 0.4 . . . C) 0.0150 . . . D) 0.1785 . . . E) 0.8215
I chose option (C), and got half credit, which is confusing.
7) An insurance company estimates that it should make an annual profit of $140 on each homeowner's policy written, with a standard deviation of $6600. If it writes 10,757 of these policies, what is the probability that the company will be profitable? Assume that policies are independent of each other and that the company's total profit follows a Normal model. (Choose one of the following.)
A) 0.955 . . . B) 0.977 . . . C) 0.014 . . . D) 0.986 . . . E) 0.023
I chose answer (B), which was wrong. I assume my error was computational, but I'm not sure how that was achieved.
Instructions: Find the expected value of the random variable. Round to three decimal places.
18) You have arranged to go campling for two days in March. You believe that the probability that is will rain on the first day is 0.5. If it rains on the first day, the probability that it also rains on the second day in 0.5. If it doesn't rain on the first day, the probability that it rains on the second day is 0.4.
Let the random variable X be the number of rainy days during your camping trip. Find the expected value of X. (Choose one of the following.)
A) mu = 1.15 . . . B) mu = 0.95 . . . C) mu = 0.7 . . . D) mu = 0.75 . . . E) mu = 1
I chose option (C) and got it wrong. Option (B) was circled on my test. I would appreciate a hint on how this answer was achieved.
Thank you!
Instructions: Determine whether the events are independent and give a reason.
2) The table below describes the smoking habits of a group of asthma sufferers.
Code:
|-------+--------+--------+--------+-------|
| | Non- | Light | Heavy | |
| | smoker | smoker | smoker | Total |
|-------+--------+--------+--------+-------|
| Men | 333 | 90 | 76 | 499 |
|-------+--------+--------+--------+-------|
| Women | 304 | 89 | 74 | 467 |
|-------+--------+--------+--------+-------|
| Total | 637 | 179 | 150 | 966 |
|-------+--------+--------+--------+-------|A) Yes, because each of the joint probabilities is equal to the product of the marginal probabilities.
B) No: P(male & heavy smoker) = 0.079 and P(female & heavy smoker) = 0.077. These are not equal.
C) No: overall, 15.5% of the group are heavy smokers, but 15.2% of the men are heavy smokers. These are not equal.
D) Yes: the percentage of women in each smoking category is the same as the percentage of men in each smoking category.
E) Yes: a heavy smoker cannot be both a man and a woman.
I chose option (D). I have no idea why this I got wrong. I'm assuming the answer is the opposite...? A little help?
Instructions: Find the indicated probability.
5) A tennis player makes a successful first serve 65% of the time. Assume that each serve is independent of the others. If she serves four times, what is the probability that she does not make all of her first serves? (Choose one of the following.)
A) 0.65 . . . B) 0.4 . . . C) 0.0150 . . . D) 0.1785 . . . E) 0.8215
I chose option (C), and got half credit, which is confusing.
7) An insurance company estimates that it should make an annual profit of $140 on each homeowner's policy written, with a standard deviation of $6600. If it writes 10,757 of these policies, what is the probability that the company will be profitable? Assume that policies are independent of each other and that the company's total profit follows a Normal model. (Choose one of the following.)
A) 0.955 . . . B) 0.977 . . . C) 0.014 . . . D) 0.986 . . . E) 0.023
I chose answer (B), which was wrong. I assume my error was computational, but I'm not sure how that was achieved.
Instructions: Find the expected value of the random variable. Round to three decimal places.
18) You have arranged to go campling for two days in March. You believe that the probability that is will rain on the first day is 0.5. If it rains on the first day, the probability that it also rains on the second day in 0.5. If it doesn't rain on the first day, the probability that it rains on the second day is 0.4.
Let the random variable X be the number of rainy days during your camping trip. Find the expected value of X. (Choose one of the following.)
A) mu = 1.15 . . . B) mu = 0.95 . . . C) mu = 0.7 . . . D) mu = 0.75 . . . E) mu = 1
I chose option (C) and got it wrong. Option (B) was circled on my test. I would appreciate a hint on how this answer was achieved.
Thank you!
