Statistics and Probability Answers

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1.Two cards are drawn from a deck, at random, in succession and without replacement.
a.What is the probability that the first draw is an ace?
b.What is the probability that both the first and the second draws are aces?

A certain type of new business succeeds 30 % of the time. Suppose that three such businesses open.
a) What is the probability that all three businesses succeed?



b) What is the probability that no business succeeds?



c) What is the probability that exactly one business succeeds?



d) Compute the mean and standard deviation for this problem.

employees in a large accounting firm claim that the mean salary of the firm's accounting is less than that of the competitors mean salary of $45,000. a random sample of 30 of the firm's accountants have a mean salary of $43,500 with a standard deviation of $5,200. test the employees claim at 95% confidence. state your conclusion of the employees claim

Assuming that half the population is vegetarian so that the chance of an individual being a vegetation is ½ and assuming that 100 investigators can take a sample of 10 individuals to see whether they are vegetarian, how many investigators would you expect to report that three people or less were vegetarians?

The scores of high school seniors taking the ACT college entrance examination in 2003 was, mean= 19.6 with standard deviation of 3.8. assume the distributing of the scores to be roughly
What is the probability that a single student chosen a random from all those taking the test scored 22 or higher?
Assume that the problem was to calculate the probability of randomly selected student scoring 23 or higher. would you expect the probability to increase, decrease, or remain the same?

A bag contains 3 red marbles, 5 yellow marbles and 6 orange marbles. Three marbles are drawn and NOT replaced each time. Determine the probability of drawing three yellow marbles in a row. State whether the events are dependent or independent.

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation 15. Find P3 which is the IQ score separating the bottom 3% from the top 97%?

The cost of a daily newspaper varies from city to city. However, the variation among prices
remains steady with a standard deviation of 6¢. A study was done to test the claim that the
average cost of a daily newspaper is 35¢. Twelve costs yield an average cost of 30¢ with a standard
deviation of 4¢. Do the data support the claim at the 1% level?

A study of 1000 randomly selected flights of a major airline showed that 782 of the flights arrived on time. What is the probability of a flight from this airline arriving on time?