Statistics and Probability Answers

b) A corporation takes delivery of some new machinery that must be installed and checked
before it becomes available to use. The corporation is sure that it will take no more than 7
days for this installation and check to take place. Let A be the event “it will be more than 4
days before the machinery becomes available” and B be the event “it will be less than 6 days
before the machinery becomes available.”
I. Describe the event that is the complement of event A.
II. Describe the event that is the intersection of events A and B.
III. Describe the event that is the intersection of events A and the complement of B.
IV. Describe the event that is the union of events A and the complement of B.
V. Are events A and B mutually exclusive?

01) a) State, with evidence, whether each of the following statements are true or false:
I. If A and B are independent, then A’ and B’ must be independent.
II. The probability of the union of two events cannot be less than the sum of their
individual probabilities.
III. The probability of the intersection of two events cannot be greater than either of their
individual probabilities.
IV. An event and its complement are not mutually exclusive.
V. If A and B are two events, the probability of A, given B, is the same as the probability of
B, given A, if the probability of A is the same as the probability of B.

Marco got 25% on a test out of 80. How many marks out of 80 did he earn?

William sunk 75% of the shots he made on the basket. If he threw 160 shots, how many did he miss?

An article in Technometrics (1999, Vol. 41, pp. 202–211) studied the capability of a gauge by measuring the weight of paper. The data for repeated measurements of one sheet of paper are in the following table. Construct a 99% one-sided, upper confidence interval for the standard deviation of these measurements. Assume population is approximately normally distributed.

Round your answer to 3 decimal places.

Observations

3.481 3.448 3.485 3.475 3.472

3.477 3.472 3.464 3.472 3.470

3.470 3.470 3.477 3.473 3.474


σ ≤ _____________

This is the main question has 5 parts-
At Penna Airport the probability P(A) that all passengers arrive on time for a flight is 0.70. The probability P(D) that departs on time is 0.85.
a) The probability that all passengers arrive on time for a flight and it departs on time is 0.65. b) Show that event A & D are not independent. Find P(A intersection D').
Given that all passengers for a flight arrive on time, c) Find the probability that the flight deos not depart on time.
The number of hours that pilots fly per week is normally distributed with mean of 25 hours and standard deviation. 90% of pilots fly less than 28 hours in week.
d) Find the value of standard deviation
All flights have two pilots
e) Find the percentage of flights where both pilots flew more than 30 hours last week

(3) A survey revealed that the mean cholesterol level of male athletes in Ghana aged 20 – 30 years is 180 mg/dl and the standard deviation is 43 mg/dl. If a random sample of 60 male athletes is selected from this population, what is the probability that the sample mean cholesterol level will be greater than 190 mg/dl?