statistics exercise

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project description:
1- consider a binomial experiment with 20 trials and probability of success of 0.45 on a single trial
a.-use the binomial distribution to find the probability of exact 10 successes.
b.-use the normal distribution to approximate the probability of exactly 10 successes
c- compare the results of 1 and 2.

2- based on a long experience , an airline has found that about 6% of the people making reservations on a flight from new york to chicago do not show up for the flight. suppose the airline overbooks this flight by selling 267 tickets for a flight with only 255 seats.
a) what is the probability that a person holding a reservation will show up for the flight?
b) let x= represent the number of tickets reservations. let r represent the number of people with reservations represents the probability that a seat will be available for everyone who shows up holding a reservation?
p (255 ≤ r); p(r ≤ 255); p(r ≤ 267); p(r = 255);

3- let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12-hour fast. assume that for people under 50 years old, x has a distribution that is approximately normal, with mean mu = 85 and estimated standard deviation sigma = 25. a result of x < 40 is an indication of severe excess insulin, and medication is usually prescribed.
a) what is the probability that, on a single test, x < 40?
b) suppose a doctor uses the average x-bar from two tests taken about a week apart. what can we say about the probability distribution of x-bar? what is the probability that x-bar < 40?
c) repeat part (b) for n = 3 tests taken a week apart.
d) repeat part (b) for n = 5 tests taken a week apart.
e) compare your answers to parts a, b, c, and d. how did the probabilities change as n increased? what must this imply if you were a doctor? if a patient had a test result of x-bar < 40 based on 5 tests, explain what must this imply?

4- consider an x distribution with standard deviation σ = 12.
(a) if specifications for a research project require the standard error of the corresponding x-bar (mean) distribution to be 2, how large does the sample size need to be?
(b) if specifications for a research project require the standard error of the corresponding x-bar (mean) distribution to be 1, how large does the sample size need to be?
5- the amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean $615 and standard deviation $42.
a. if $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount?
b. how much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.10?

6- porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. in healthy circles, x is approximately normally distributed with mean μ = 42 and standard deviation σ = 13. find the following probabilities. (round your answers to four decimal places.)
(a) x is less than 60
(b) x is greater than 16
(c) x is between 16 and 60
(d) x is more than 60 (this may indicate an infection, anemia, or another type of illness.)

7-fawns between 1 and 5 months old in mesa verde national park have a body weight that is approximately normally distributed with mean u= 27.2 kilograms and standard deviation 0 = 4.3 kilograms. let x be the weight of a fawn in kilograms convert each of the following x intervals to z intervals.

a). x < 30 b). 19 < x c) 32 < x < 35
convert each of the following z intervals to x intervals
d). – 2.17 < z e z < 1.28 f). – 1.99 < z < 1.44
g). if a fawn weights 14 kilograms, would you say it is an unusually small animal? explain using z values and figure 7 -12
h). if a fawn is unusually large, would you say that the z value for the weight of the fawn will be close to 0, - 2, or 3? explain.
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