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What is the probability that Lisa smiles at Milhouse on exactly three days in a month? Use a Poisson approximation to calculate the probability that Lisa smiles at Milhouse on exactly three days in
Suppose X has pmf (probability mass function) f(x)=1/5, x=1,2,3,4,5. Compute E(X) and E(X^2) and use those two results to find E[(X+2)].
At one college, GPAs are normally distributed with a mean of 2.6 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.2 and 3?
For a normal distribution, find the probability that an observation falls within 0.92 standard deviations of the mean.
Short term versus long run Short-term aberrations do not affect the long run. To illustrate, suppose that you flip a coin 10 times and you get 10 heads.
A recent study focused on the amount of money single men and single women save monthly. The information is summarized below. Assume that the population standard deviations are equal.
A life insurance company has determined that each week an average of eight claims is filed in its Nashville branch.
A regional track championship has decided that they will invite the fastest 15% of runners in their region (runners with the shortest time). The mile time of all potential runners in this region are
In a test of the drug lipitor, 16.7% of the subjects treated with 10mg of atorvastatin experienced headaches. Assume 60 subjects are randomly selected and treated with 10 mg of atorvastatin.
Use a Poisson approximation to calculate the probability that Lisa smiles at Milhouse on exactly three days in a month.
Consumer report does a study on 50 of the most popular computer printer brands. The data collected includede the reatil price ($) for each brand and its equivalent printing speed (# pages per minute
Use the binomial probability distribution when your random variable is the number of successes on n success or failure trials when the probability of success, p , is the same for each trial, and the
Assume the probability that a newborn is a boy is 51 %, that is, p = 0:51. Suppose a family has 8 children. (a) What is the distribution law followed by the number of boys in such a family? (b) Deno
Determine the mean and variance of the random variable.
Assume that the process stops once there are no red balls in the urn. Model this process as a Markov chain. Give the transition probability matrix
A sample of 2 different calculators is randomly selected from a group containing 18 that are defective and 37 that have no defects. What is the probability that the 2 calculators chosen have no defe
Let x be a random variable corresponding to the sum of the numbers on two fair dies(Hints, 2,3,4,....,12), Find the probability of P{x<8}.
A population has a known standard deviation of 25. A simple random sample of 49 items is taken from the selected population. The sample mean (x-bar) is 300. What is the margin of error at the 95% co
Body mass index for newborns follows a normal distribution with a mean of 14 and standard deviation of .95. A doctor delievers 3 babies a day. What is the probability the average body mass index is
One person has 3 dollars to gamble; each time he uses only one dollar, the probability is 60% to lose and 40% to win. If he accumulates 5 dollars or loses 3 dollars, he will stop the gamble. Using t
An extensive survey of customers of three major cable companies(A,B,and C) found the following: Company A will keep 71% of its customers, 12% will move to B and the rest will move to C
Determine the probability that exactly two of these vehicles require warranty service. Compute the mean and standard deviation of this probability distribution
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 241 customers on the number of hours cars are parked and the amount they are charged.
Find the distribution of the market by finding the steady state vector.