1. Find the following probabilities:
(A) Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.4 and P(A or B) = 0.65, find P(B).
(B) Events A and B are defined on a common sample space. If P(A) = 0.30, P(B) = 0.50, and P(A or B) = 0.60, find P(A and B)
2. A bag of jelly belly candies contains the following colored jelly beans: red (5), blue (2), orange (5), brown (21), green (10), and yellow (6). Construct the probability distribution for x.
3. Find the mean and standard deviation of the following probability distribution:
x 1 2 3
P(x) 0.2 0.6 0.2
4. Classify the following as discrete or continuous random variables.
(A) The number of people in India
(B) The number of planets in the universe.
(C) The blood pressures of patients admitted to a hospital in one day
(D) The length of a centipede
5. In testing a new drug, researchers found that 1% of all patients using it will have a mild side effect. A random sample of 12 patients using the drug is selected. Find the probability that:
(A) exactly one will have this mild side effect
(B) at least one will have this mild side effect.
6. X has a normal distribution with a mean of 70.0 and a standard deviation of 3.0. Find the following probabilities:
(A) P(x < 68.0)
(B) P(68.0 < x < 72.0)
7. Find the value of z such that 25% of the distribution lies between it and the mean
8. Assume that the average annual salary for a worker in the United States is $41,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $7,000. Find the following:
(A) What percentage of Americans earn below $27,000?
(B) What percentage of Americans earn above $43,000?
The solution provides step by step method for the calculation of binomial and normal probabilities. Formula for the calculation and interpretations of the results are also included.