It is known that P(80 - a X 80 + b) = 0.6463. This information is shown in the f

Question

It is known that P(80 - a X 80 + b) = 0.6463. This information is shown in the figure below Show that the area of the shaded region is 0.118 A diagnostic test for a disease is such that it correctly detects the disease in 90% of the individuals who actually have the disease. Also, if a person docs not have the disease, the test will report that he or she docs not have it with probability 95%. Only 1% of the population has the disease in question. If a person is chosen at random from the population and the diagnostic test indicates that she has the disease, what is the probability that she docs, in fact, have the disease? Show all of your work. An unfair coin, with probability of heads equal to 1/4, is flipped 30 times. Find the probability of exactly 10 heads. What arc the mean and variance for the number of heads? Find the probability of getting more than 4 heads. a. Only 1 in 1000 adults is afflicted with a rare disease for which a diagnostic test has been developed. The test is such that when an individual actually has the disease, a positive result will occur 99% of the time, whereas an individual without the disease will show a positive test result only 2% of the time. If a randomly selected individual is tested and the result is positive, what is the probability that the individual has the disease? An individual has 3 different email accounts. Most of her messages, in fact 70%, come into account #1, whereas 20% come into account #2 and the remaining 10% into account #3. Of the messages into account #1, only 1% are spam, whereas the corresponding percentages/or accounts #2 and #3 are 2% and 5%, respectively. What is the probability that a randomly selected message is spam? If P(A) - 0.4, P(B) - 0.5, P(AUB) - 0.7. Find P{AB) Are A and B independent? Why? Are A and B Mutually exclusive? Why? For independent events P(A and B) = P(A) * P(B) For mutually exclusive events P(A B) = 0 Each of six randomly selected cola drinkers is given a glass containing cola S and one containing cola F. The glasses are identical in appearance except for a code on the bottom to identify the cola. Suppose there is actually no tendency among cola drinkers to prefer one cola to the other. Find the probability that 3 people prefer S; at most one prefer S. The random variable X is normally distributed with mean 80 and variance 100. Find

Explanation / Answer

9.

C)

Note that the total area of the curve is 1.

Hence,

P(x<80-a) + 0.6463 + P(x>80+b) = 1

As P(x>80+b) = 2P(x<80-a)

Then

P(x<80-a) + 0.6463 + 2P(x>80-a) = 1

0.6463 + 3P(x>80-a) = 1

3P(x>80-a) = 0.3537

P(x>80-a) = 0.1179 = 0.118 [DONE]

which is the shaded area.

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