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    Probability

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    Probability Questions

    51. The following cross tabulation shows household income by educational level of the Head of household (Statistical Abstract of the United States:2002) Under 25.0- 50.0- 75.0- 100 or Education Level 25 49.9 74.9 99.9

    Probability Questions

    31. Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = .30 and P(B) = .40 a. What is P(A B)? b. What is P(A | B)? c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutua

    Substitution Matrix

    Smith-Walterman Alignment. See attached file for full problem description. Suppose two sequences each 1000 amino acids long are aligned with Smith-Waterman alignment using the PAM250 matrix, what is the score for the following alignment: MCVESVNREMSPLV LVLKALCTKVPELI Is this a significant alignment score? Y/N Briefl

    High School Statistics Sample Problems

    1. Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. 1.1) In bridge, 6 of one suit, 4 of another, and 3 of another A) .0133 B) .0022 C) .0060 D) .00055 1.2) In poker, a flush (5 in same suit) in any suit A) .00198 B) .

    Calculation of Expected Opportunity Loss

    The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature. States A1 A2 A3 1 12 -2 8 2 4 10 5 where: S1 is state of nature 1 A1 is action alternative 1 S2 is state of nature 2 A2 is action alternative 2 A3 is action alternative 3 Referring to t

    Coin flipping problem and SSE calculation

    A coin is flipped 5 times in a row. What is the probability that it will come up heads all 5 times? For the data in question above, calculate the Sum of Squares Error (SSE).

    Inverted Gamma Distribution

    5. If X gamma(alpha, beta), then Y=1/X has the inverted gamma distribution. (a) Derive the form of the pdf; (b) verify that it is a pdf; (c) and calculate the mean and variance 6. Let X be a positive random variable, i.e. P(X greater or less than 0) = 0. Prove that E(ln(1/x) greater of less than ln(1/E(X)).

    Statistics Practice

    Let X have a binomial distribution. Find the distribution of Y. See attached file for full problem description.

    Roulette Probabilities

    A success, s in Bernoulli trials is often derived from the collection of outcomes. For example, an American roulette wheel consists of 38 numbers, of which 18 are black, 18 are red, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any one of the 38 numbers. If you're interested in which num

    What is the probability that between 2 and 6 customers inclusive want hot peppers?

    1) Elly's hot dog emporium is famous for chili dogs. Some customers order hot dogs with hot peppers, while many do not care for the extra zest. Elly's latest taste test indicates that 30% of the customers ordering her chili dogs order it with hot peppers. Suppose 18 customers are selected at random. What is the probability that

    Probability

    (27) A company is in the process of hiring new employees for its sales force. The Human Resource manager estimates that the following are the probabilities of how many sales people will be hired during the next three months: No. To Be Hired Probability 0 5% 1 10% 2 20% 3 20% 4 25% 5 10% 6 10% What is the expected numb

    Airport scanning Bayesian probability

    1. Suppose an airport scanning device has 98% accuracy in detecting certain kinds of metal objects (98% of people carrying these objects are correctly identified as carriers and 98% of people not carrying them are correctly identified as non-carriers). Suppose that 1% of all travelers actually carry such metal objects. For the 1

    Statistical Analysis of Deaths in the U.S.

    1. In a recent year, there were approximately 97,000 deaths in the United States (total population 281 million) due to accidents. Approximately 25,000 of these accidental deaths involved people age 75 or older. Roughly 42,000 of these deaths were due to automobiles and 17,000 involved falls. a. Find the overall death rate for

    The classic question of probability Part 2

    Monty would often offer contestants money in exchange for whatever was behind their chosen door. If you knew the prize hidden behind one of the doors to be worth $30,000, how much would Monty have to offer to convince you to abandon your original choice? After Monty revealed a booby prize, how much would he have to offer you t

    The classic question of probability Part 1

    The Monty Hall Problem. In the classic television game show, "Let's Make A Deal," contestants were asked to choose one of three doors. Behind one of these doors was a valuable prize; the other two concealed "booby prizes" which contestants wanted to avoid. After a contestant chose one of the doors, Monty Hall (who knew where t

    Binomial and Normal Variable

    1. A manufacturer of window frames knows from long experience that 5 percent of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 20 window frames: a. None will need adjustment? b. At least one will need adjustment? More than two will need

    Business Statistics - Probability, Sampling,

    See attached file for full problem description. — 1. The 1996-97 mean annual starting salary for accounting majors was $30,393 (U.S. News On-line. December 28, 1997). Assume that for the population of graduates with accounting majors the mean annual starting salary is pr = $30,393 and the standard deviation is 0 = $2000

    Probability Questions: What is the probability of acceptance into a school?

    1. A school in Bangkok requires that students take an entrance examination. After the examination, there is a drawing where 5 students are randomly selected from each group of 40 for automatic acceptance into the school, regardless of their performance on the examination. The drawing consists of placing 35 red and 5 green pie

    Permutaion and Combination

    1. A group of 3 students is to be selected from a group of 12 students to take part in a class in cell biology. a. In how many ways can this be done? b. In how many ways can the group who will not take part will be chosen? 2. After studying all night for a final exam, a bleary eyed student randomly grabs 2 soc

    Probability Questions in Excel

    1. A landscape contractor bids on jobs where he can make 3000 profit. Probabilities of getting one, two, three or four jobs per month are shown. #Jobs 1 2 3 4 Probability 0.2 0.3 0.4 0.1 Find contractor's expected profit per month 2. If a player rolls two dice and gets a sum of 2 or 12 she wins 20.00. If the person get a

    Probability of Side Effects of Anesthetics

    Anesthesia question (I prefer you do not use the Student t test nor Chi-square) A side effect of a certain anesthetic used in surgery is the hiccups, which occurs in about 10% of the cases. If three patients are scheduled for surgery today and are to be administered this anesthetic, compute the probability that: a. All thr

    Explanations for Various Probability Questions

    Question D An experiment consists of tossing an ordinary coin five times. Recall that an experiment can produce one or more sample spaces depending on what we consider our outcome to be. Consider the following 4 sets: (a) S = {zero heads, one head, two heads, four heads, five heads} (b) S = {no heads, no tails, at least one

    Probability of Radio Failure

    A radio has a failure rate of .22 x 10-5. If the radio operates for 1000 hours, what is the probability that the radio will not fail? Please work as an example and show work.

    Poisson Statistics Distribution for Failure of a System

    A system is tested for 10,000 hours and experiences 2 failures. Its failure rate is believed to be Poisson distributed. a. What is the probability of no failures in 5000 hours of operation of this system? b. If two of these systems are operated 1500 hours each, what is the probability of no failures in the two systems?

    Probability questions about students in various classes

    4. Of the 47 people who answered "yes" to a question, 8 were male. Of the 100 people who answered"no" to the question, 12 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male? A) 0.456 B) 0.401 C) 0.136 D) 0.17 5. A teacher designs a test so a

    Normal/approximation to Binomial

    Disregard #3- Part C. Thanks 1. If you determine that for the graph of a standard normal distribution the cumulative area to the left of a z core is 0.4, what is the cumulative area to the right of that z score? 2. Assume that the readings on the thermometers are normally distributed with a mean of 0 degree and a standard