Question

1. The service manager for Air Canada is uncertain about the time needed for the ground crew to turn an airplane around from the time it lands until it is ready to take off. He has been given information from the operations supervisor indicating that the times seem to range between 20 and 45 minutes. Without any further information, the service manager will apply a uniform distribution to the turnaround. (a) Define the density distribution/function. (b) What is the probability that the crew can get a plane ready to fly again after it lands between 28 and 35 minutes? (c) What is the mean and standard deviation of the probability distribution?

2. Steve is about to write a test with 10 true or false questions and 15 multiple choice questions. Steve has been studying hard so we’ll give a 75% chance of getting any of the 25 questions right. Assume all the questions are independent of each other. (a) What is the probability that Steve gets exactly two thirds of the multiple choice questions right? (b) What is the probability that Steve gets exactly half the true or false questions right AND gets exactly two thirds of the multiple choice questions right? (c) If the test was all multiple choice (i.e. 25 questions), use the normal approximation to estimate the probability that Steve get between 15 and 20 questions right.

3. Suppose that the weight of Florida navel oranges is normally distributed with mean µ = 8 ounces, and standard deviation σ = 1.5 ounces. (a) State the model in notation form. (b) (2 points) What proportion of oranges weigh more than 11.5 ounces? (c) What proportion of oranges weigh less than 8.7 ounces? (d) What proportion of oranges weigh between 6.2 and 7 ounces? (e) What are the median, mode, first quartile, third quartile and IQR for the oranges? (f) Find the 80th percentile of the distribution of X. (g) Suppose another strain of navel oranges from California has a mean µ = 8.5 ounces, and standard deviation σ = 1.7 ounces. A Florida orange is randomly selected and weighs 12 ounces, while a California orange is randomly selected and weighs 13 ounces. Which one strain of orange is ”relatively” bigger for its average size?

4. A radioactive source emits 4 particles on average during a five-second period. (a) (1 point) What are the mean and standard deviations of the distribution of the emitting particles? (b) (2 points) Calculate the probability that it emits 3 particles during a 5-second period. (c) (2 points) Calculate the probability that it emits at least one particle during a 5-second period. (d) (2 points) During a ten-second period, what is the probability that 6 particles are emitted?

5. Assume that the probability that a person is infected with COVID is 0.02 in your area. If you randomly select people off the street, (a) what is the probability that the first person to test positive is the seventh person tested? (b) How many people would you have test before you discover your first person to test positive? (c) If you alow plus or minus one standard deviation, what is the range you might expect the first person to test positive? (Note: For all questions, assume the test is 100 percent accurate!)

Answer 1

Answer:-

Given That:-

1. The service manager for Air Canada is uncertain about the time needed for the ground crew to turn an airplane around from the time it lands until it is ready to take off. He has been given information from the operations supervisor indicating that the times seem to range between 20 and 45 minutes. Without any further information, the service manager will apply a uniform distribution to the turnaround.

(a) (2 points) Define the density distribution/function.

Define the density distribution/function

(b) (2 points) What is the probability that the crew can get a plane ready to fly again after it lands between 28 and 35 minutes?

What is the probability that the crew can get a plane ready to fly again after it lands between 28 and 35 minutes

p(x) = (35-28)/(45-20)

= 7/25

c) (2 points) What is the mean and standard deviation of the probability distribution?

What is the mean and standard deviation of the probability distribution

= 65/2

= 32.5