Statistics and Probability Answers

The probability that a new airport will get an award for its design is 0.16, the
probability that it will get an award for the efficient use of materials is 0.24 and the
probability that it will get both the awards is 0.11.
(a) what is the probability that it will get atleast one of the two awards?
(b) what is the probability that it will get only one of the two awards?

A box containing 8 light bulbs of which 3 are defective. A bulb is selected from the
box and tested. If it is defective, another bulb is selected and tested until a nondefective
bulb is chosen. Find the expected number and variance of bulbs chosen.

24. Rosalie Friend (2001), and educational psychologist, compared three methods of teaching writing. Students were randomly assigned to three different experimental conditions involving different methods of writing a summary. At the end of the two days of instructions, participants wrote a summary. One of the ways it was scored was the percentage of specific details of information it included from the original material. Here is a selection from her article describing one of the findings:

The effect of summarization method on inclusion of important information was significant F(2, 144) = 4.1032, p < .019. The mean scores (with standard deviations in parantheses) were as follows: Argument Repetition, 59.6% (17.9); Generalization, 59.8% (15.2); and Self-Reflection, 50.2% (18.0). (p.14)

a. Explain these results to a person who has never had a course in statistics.
b. Using the information in the preceding description, figure the effect size for the study.

National Bank is considering changing the day for scheduled maintenance for the automatic teller machine (ATM) in the lobby. The average number of people using it between 8 and 9 A.M is 60, except on Friday, when the average is 90. The management decision must balance the efficient use of maintenance staff while minimizing customer inconvenience.
i) Does knowledge of the two average figures affect the manager’s expected value (for inconvenienced customers)?
ii) Taking the data for all days together, the relative probability of inconveniencing 90 customers is quite small. Should the manger expect many inconvenienced customers if the maintenance day is changed to Friday?

The administration department of PIMS Hospital Islamabad surveyed the number of days 400 randomly chosen patients stayed in the hospital after an operation.
The data are:
Days (of hospital say): 1-3 4-6 7-9 10-12 13-15 16-18 19-21 22-24
Frequency: 36 18 88 42 18 18 8 10
a) Calculate the standard deviation and mean.
b) According to Chebyshev’s theorem, how many stays should be between 0 and 17 days? How many are actually in that interval?
c) How many stays can we expect between 0 and 17 days?

General Co. has designed a new tire, and they don’t know what the average amount of tread life is going to be. The tread life is normally distributed with a standard deviation of 295.5 kilometers.
i) If the company samples 800 tires and records their tread life, what is the probability the sample mean is between the true mean and 350 kilometers over the true mean?
ii) How large a sample must be taken to be 95 percent sure the sample mean will be within 150 kilometers of the true mean?

Mehwish will graduate in 3 months with a Master’s degree in Business Administration. Her college’s placement office indicates that the probability of receiving a job offer as the result of any given interview is about 0.08 and is statistically independent from interview to interview.
i) What is the probability that Mehwish will not get a job offer in any of her next four interviews?
ii) If she has three interviews per month, what is the probability that she will have at least one job offer by the time she completes her studies?
iii) What is the probability that in her next five interviews she will get job offers on the third and fifth interviews only?

Three cooks, A, B and C bake a special kind of cake, and with respective probabilities 0.02, 0.03, and 0.05 it fails to rise. In the restaurant where they work, A bake 50 percent of these cakes, B 30 percent and C 20 percent. What proportion of failures is caused by A

One half percent of the population has a particular disease. A test is developed for the disease. The test gives a false positive 3% of the time and a false negative 2% of the time. (a). What is the probability that Joe (a random person) tests positive? (b). Joe just got the bad news that the test came back positive; what is the probability that Joe has the disease?

A stamping machine produces ‘can tops’ whose diameters are normally distributed with a standard deviation of 0.02 inch. At what nominal mean diameter should the machine be set, so that no more than 9 % of the ‘can tops’ produced have diameters exceeding 3.5 inches?