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In the Powerball® lottery, the player chooses five numbers from the first field of 59 numbers and one "Powerball" number from the second field of 35 numbers. A player wins the jackpot if all six of the player's numbers match the six winning numbers.
(a) How many different possible ways are there select the six numbers?
(b) How many tickets would someone have to purchase to have at least a one in a million chance of winning the jackpot?
(c) What is the probability that none of the player's numbers match any of the six winning numbers? (Assume this player only has one ticket.)
(d) The player wins the second prize if the player matches the first five numbers but does not match the Powerball. The player wins third prize if the player matches the Powerball but only matches four of the other five numbers. What is the probability that a player who buys a single ticket will win at least third prize?
The sampling distribution of mean score is approximately Normal. It has mean. What is its standard deviation?
Do these data provide sufficient evidence to reject the claim made by Creative Good? Two sample F-test for the ratio of population variances
Perform exploratory data analysis on all variables in the data set. Realizing that you have six groups, be sure that your exploratory analysis is broken down by group. When possible, include appropriate graphs to help illustrate the dataset.
The following frequency distribution reports the number of frequent flier miles, reported in thousands, for employees of Brumley Statistical Consulting, Inc. during the first quarter of 2004.
If only one spark plug fails, the plane will shake and not climb higher, but it can be landed safely. What is the probability that this happens? Calculate using the appropriate formula.
The table shows the retail market share of passenger cars from Ford Motor Company as a percent of the US market.
Develop the "best" regression model possible using this set of variables to help you predict the Risk. State your final model. Interpret the coefficients for the model (i.e. what do the numbers mean?).
Ace Machine Works estimates that the probability its lathe tool is properly adjusted is 0.8. When the lathe is properly adjusted, there is a 0.9 probability that the parts produced pass inspection.
if a gambler rolls a dice twice to get a sum of 10, he wins $10. and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of the game?
Explain whether the authors used a population or a sample. Explain how this could have affected the results. If a sample was used, was it representative of the entire population? Why or why not?
A government worker claims that the standard deviation of the mean weight of all US Postal Service shipments is 0.40 pounds. If a hypothesis test is performed, how should you interpret a decision
Random samples of size 64 are taken from a large population whose mean is 160 and whose standard deviation is 25. What is the mean of the sampling distribution of the sample mean?
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