Statistics and Probability Answers

In Islamabad city the mean number of power outages is 4 per month. Find the
probability that in a given month,
a. There are exactly 3 outages
b. There are more than 2 outages.

a. A programmer is taking a two-hours-time-limit makeup examination. Suppose the probability
that the programmer will finish the exam at most y hours is y/3, for all 0 ≤ y ≤ 2. Given that the
student is still working after 1.75 hours, what is the conditional probability that the full time is
used?
b. A multiple choice test has 7 questions with 3 wrong choices and 1 correct choice each. How many
ways are there to answer the test? What is the probability that two papers have the same answers?

In each lot 200 items, two items are tested and the lot is rejected if either of the tested items is found
defective.
(a) Find the probability that a lot with k defective items is accepted.
(b) Suppose that when the production process malfunctions, 50 out of 100 items are defective.
In order to identify when the process is malfunctioning, how many items should be tested
so that the probability that one or more items are found defective is at least 99%?

Four of the Statistics for Business and Economics students submitted an entry to a Math contest at the faculty. A total of 24 entries were submitted. Six of the entries will move on to the next round.
(i)How many Statistics for Business and Economics students are expected to move to the next round?
(ii)What is the hypergeometric probability that fewer Statistics for Business and Economics students than expected will make it to the next round?

A chip manufacturer tests the microprocessors produced from the production line process. The company made a statement (claim) that only 4% of its microprocessor production was damaged. To test whether the claim is true, a study was conducted by taking a sample of 577 microprocessors, of which 37 were damaged. Can the statement (claim) be rejected or accepted with a 99% confidence level?

From the study concluded that 7.3% of a population suffering from osteoporosis (porous bone disease). A new technique was developed to test a large individual sample, which consists of two groups of people. The first group is the one who is known to suffer from osteoporosis, and the second group is the group that is confirmed not to suffer from osteoporosis from tests using the old technique. The result is the probability of someone who is confirmed to have osteoporosis, producing a positive test is 95%. While those not suffering from osteoporosis, the probability resulting in a positive test with the new technique is 2%.

i) What is the probability that a person will produce a positive test for osteoporosis, regardless of whether he has the disease, or not (group 1, and group 2).

ii) What is the probability that someone does not have osteoporosis, given that the test results with this new technique are positive?

At a large university, 25% of students are over 21 years old. In a sample of 400 students, calculate the probability that more than 110 of them are over 21 years old.

Statistics department data show that 20% of Pakistani age 18 and over holds a certificate of matriculation. If 10 Pakistani national age 18 and above are randomly selected, find the probability that at least 3 will have certificates of matriculation.

In a Internee program at Airline Company, 60 percent of the internees are female and 40 percent
male. 80 percent of the females are business students, and 65 percent of the males are business
students.
a) An internee is selected at random. What is the probability that the person selected is a female
who is not a business student?
b) Are gender and field of study, independent in this case? Why?

A firm purchases a microchip used in the manufacturing of LED screens from four different
suppliers. TechZone supplies 30 percent of the total microchips, Advance Electronics 25 percent,
PSP importers 18 percent, and TechParts inc. 32 percent. TechZone tends to have the best
quality, as only 3 percent of its microchips arrive defective. Advance Electronics chips are 4
percent defective, PSP importers chips are 7 percent defective, and Parts Inc. are 6.5 percent
defective.
a) If a random chip is selected, what is the probability that the chip is defective
b) A defective chip was discovered in the latest shipment. What is the probability that it came
from TechZone supplies?
c) A defective chip was discovered in the latest shipment. What is the probability that it came
from Parts Inc.?