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Probability and chance

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A prison has 20 balls, 10 black and 10 white. The prisoner is to arrange the balls in 2 boxes. All of the balls must be used and there must be at least one ball in each box. An executioner will select one box at random and then one ball at random from the chosen box. The prisoner is set free if the ball is white and executed if the ball is black. How should the prisoner arrange the balls in the boxes to maximize his/her chance of being set free?

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In one box, the prisoner arrange one white ball inside; in the ...

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This provides an example of a probability puzzle regarding maximizing chance.

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In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.10 hours per week playing organized sports. The population's standard deviation is 2.00 hours per week. Based on a sample of 64 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates.

(a) Compute the standard error of the sample mean. (Round your answer to 2 decimal places.)

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(b) What is the chance HLI will find a sample mean between 4.4 and 5.8 hours? (Round z value to 2 decimal places. Round your answer to 4 decimal places.)

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(c) Calculate the probability that the sample mean will be between 4.7 and 5.5 hours. (Round z value to 2 decimal places. Round your answer to 4 decimal places.)

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(d) How strange would it be to obtain a sample mean greater than 7 hours?

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