35. The Center for Medicare and Medical Services reported that there were 295,000 appeals for hospitalization and other Part A Medicare service. For this group, 40% of first-round appeals were successful (The Wall Street Journal, October 22, 2012). Suppose 10 firstround appeals have just been received by a Medicare appeals office.
PLEASE SHOW HOW TO COMPUTE ANSWERS IN EXCEL USING EXCEL FORMULAS
a. Compute the probability that none of the appeals will be successful.
b. Compute the probability that exactly one of the appeals will be successful.
c. What is the probability that at least two of the appeals will be successful?
d. What is the probability that more than half of the appeals will be successful?
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A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the probability that the disease will be detected by the test is 0.93. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.03. It is estimated that 3% of the population who take this test have the disease. (Round your answers to three decimal places.)
(a) If the test administered to an individual is positive, what
is the probability that the person actually has the disease?
(b) If an individual takes the test twice and the test is positive
both times, what is the probability that the person actually has
the disease? (Assume that the tests are independent.)
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As a quality control manager, you are responsible for checking the quality level of AC adapters for tablet PCs that your company manufactures. You must reject a shipment if you find 5 defective units. Suppose a shipment of 46 AC adapters has 12 defective units and 34 non defective units. Complete parts (a) through (d) below assuming you sample 15 AC adapters. a) What is the probability that there will be no defective units in the shipment? b) What is the probability that there will be at least 1 defective unit in the shipment? c) What is the probability that there will be 5 defective units in the shipment? d) What is the probability that the shipment will be accepted?
In: Math
Two rolls of a fair die. Let x and y be the results of the two rolls, and let z = x + y.
(a) Find P[x = 4, y = 3], P[x > 3, y = 5].
(b) Find P[z = 7], P[z = 5], P[z = 3].
(c) Find the probability that at least one 6 appears given that z = 8.
(d) Find the probability that x = 6 given that z > 8.
(e) Find the probability that z = 7 given that at least one 4 was rolled. (f) Find the probability that z > 7 given that y = 4.
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The length of western rattlesnakes are normally distributed with a mean of 60 inches and a standard deviation of 4 inches. Enter answers as a decimal rounded to 4 decimal places with a 0 to the left of the decimal point.
A) Suppose a rattlesnake is found on a mountain trail: a. What is the probability that the rattlesnakes' length will be equal to or less than 54.2 inches?
B) What is the probability its' length will be equal to or greater than 54.2 inches?
C) What is the probability that the rattlesnakes' length will be between 54.2 inches and 65.8 inches?
D) Suppose a nest of 16 rattlesnakes are found on the mountain trail:
What is the probability that the average length of the rattlesnakes will be 60.85 inches or more?
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A box in a certain supply room contains four 40-W lightbulbs, five 60-W bulbs, and seven 75-W bulbs. Suppose that three bulbs are randomly selected. (Round your answers to four decimal places.)
(a) What is the probability that exactly two of the selected bulbs are rated 75-W?
(b) What is the probability that all three of the selected bulbs have the same rating?
(c) What is the probability that one bulb of each type is selected?
(d) Suppose now that bulbs are to be selected one by one until a 75-W bulb is found. What is the probability that it is necessary to examine at least six bulbs?
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[Counting and Probability] Consider the experiment of flipping a coin four times.
a. Using a tree, determine the probability of one or two tails, with a biased coin with P(H) = 2/3. Compare to the probability with an unbiased coin
b. [Bayes’ Rule] Using the results of the part a suppose we have
two coins, one unbiased, and a biased coin with P(H) = 2/3. We
select a coin at random, flip it three times, and observe either
one or two tails. What is the probability we started with the
biased coin?
[Hint: use a two-level tree, with the second level using the
probabilities from a.]
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In a town, 36% of the citizens contributed to the Republicans, 46% contributed to the Democrats, and 12% contributed to both. What percentage contributed to neither party?
A box contains 4 white, 3 red, and 3 black marbles. One marble is chosen at random, and it is not black. Find the probability that it is white. (Enter your answer as a fraction.)
Suppose that 90% of drivers are "careful" and 10% are
"reckless." Suppose further that a careful driver has a 0.2
probability of being in an accident in a given year, while for a
reckless driver the probability is 0.3. What is the probability
that a randomly selected driver will have an accident within a
year? (Enter your answer to two decimal places.)
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Your friend texted you a question. You did some research and found that a Minifig is a package containing one figurine. You also found out that, for every 60 packs produced, 4 of those are Chip and 4 are Dale.
A) What is the probability of opening one box and getting Chip?
B) What is the probability of opening one box and getting Chip OR Dale?
C) What is the probability of opening two boxes and specifically getting Chip in the first box and Dale in the second box?
D) What is the probability of opening two boxes and getting one Chip and one Dale (in either order)?
ANSWER ALL PARTS A-D
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The U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542. Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246. A Boston worker is randomly selected. (Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)
(a) What is the probability that the worker’s annual salary is more than $60,000?
(b) What is the probability that the worker’s annual salary is less than $42,000?
(c) What is the probability that the worker’s annual salary is more than $39,000?
(d) What is the probability that the worker’s annual salary is between $43,000 and $51,000?
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