A company manufactures batteries in batches of 15 and there is a 3% rate of defects. Find the mean number of defects per batch.
An archer is able to hit the bull's eye 56% of the time. If she shoots 7 arrows, how many bull's-eyes do you expect her to get? Assume the shots are independent of each other.
A basketball player has made 66% of his foul shots during the season. Assuming the shots are independent, find the probability that in tonight's game he misses for the first time on his 6th attempt?
A basketball player has made 70% of his foul shots during the season. If he shoots 5 foul shots in tonight's game, what is the probability that he doesn't make all of the shots?
Find the probability of at least 2 girls in 8 births. Assume that male and female births are equally likely and that the births are independent events.
A beginning archer is able to hit the bull's-eye 39% of the time. If she shoots 6 arrows, what is the probability that she gets at most 3 bull's-eyes? Assume each shot is independent of the others.
A tennis player makes a successful first serve 60% of the time. If she serves 8 times, what is the probability that she gets more than 3 first serves in? Assume that each serve is independent of the others.
II. Mixed Practice
Dr. Fidgit developed a test to measure boredom tolerance. He administered it to a group of 20,000 adults between the ages of 25 and 35. The possible scores were 0, 1, 2, 3, 4, 5, and 6, with 6 indicating the highest tolerance to boredom. The following is the probability distribution:
?
a) Find ?
b) Find ?
c) Find ?
"One in 10 high school graduates in the state of Florida sends an application to the University of Florida," says the direct of admissions. If Florida has 120,000 high school graduates next year, how many applicants would they expect?
Consider a small ferry that can accommodate cars and buses. The toll for cars is $3 and the toll for buses is $10. Let X and Y denote the number of cars and buses, respectively, carried on a single trip. Suppose the X and Y are independent and have the following probability distributions:
X = # of cars Y = # of buses
Compute the mean, variance and standard deviation of the number of cars on the ferry.
Compute the mean and variance of the number of buses on the ferry.
Compute the mean and variance of total number of vehicles on the ferry.
Compute the mean and variance of the total amount of money collected on the ferry.
Which type of vehicle is bringing in more money?
How much more should we expect from that vehicle per trip?
What is the variance of this amount?