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Chapter 8: Q158SE (page 452)
Consider the discrete probability distribution shown here.
x | 10 | 12 | 18 | 20 |
p | .2 | .3 | .1 | .4 |
a. Calculate and .
b. What is ?
c. Calculate .
d. What is the probability that xis in the interval ?
(a)
(b)
(c)
(d) The required probability is 0.5.
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Optimal goal target in soccer. When attempting to score a goal in soccer, where should you aim your shot? Should you aim for a goalpost (as some soccer coaches teach), the middle of the goal, or some other target? To answer these questions, Chance (Fall 2009) utilized the normal probability distribution. Suppose the accuracy x of a professional soccer player鈥檚 shots follows a normal distribution with a mean of 0 feet and a standard deviation of 3 feet. (For example, if the player hits his target,x=0; if he misses his target 2 feet to the right, x=2; and if he misses 1 foot to the left,x=-1.) Now, a regulation soccer goal is 24 feet wide. Assume that a goalkeeper will stop (save) all shots within 9 feet of where he is standing; all other shots on goal will score. Consider a goalkeeper who stands in the middle of the goal.
a. If the player aims for the right goalpost, what is the probability that he will score?
b. If the player aims for the center of the goal, what is the probability that he will score?
c. If the player aims for halfway between the right goal post and the outer limit of the goalkeeper鈥檚 reach, what is the probability that he will score?
Independent random samples from two populations with standard deviations , respectively, are selected. The sample sizes and the sample means are recorded in the following table:
Sample 1 | Sample 2 |
a. Calculate the standard error of the sampling distribution for Sample 1.
b. Calculate the standard error of the sampling distribution for Sample 2.
c. Suppose you were to calculate the difference between the sample means . Find the mean and standard error of the sampling distribution .
d. Will the statistic be normally distributed?
Given the following values of , , and , form a 90% confidence interval for
a.
b.
c.
d.
The 鈥渨inner鈥檚 curse鈥� in transaction bidding. In transaction bidding, the 鈥渨inner鈥檚 curse鈥� is the miracle of the winning (or loftiest) shot price being above the anticipated value of the item being auctioned. The Review of Economics and Statistics (Aug. 2001) published a study on whether shot experience impacts the liability of the winner鈥檚 curse being. Two groups of a stab in a sealed-shot transaction were compared (1)super-experienced stab and (2) less educated stab. In the super-experienced group, 29 of 189 winning flings were above the item鈥檚 anticipated value; 32 of 149 winning flings were above the item鈥檚 anticipated value in the less-educated group.
Entrepreneurial careers of MBA alumni. Are African American MBA scholars more likely to begin their careers as entrepreneurs than white MBA scholars? This was a question of interest to the Graduate Management Admission Council (GMAC). GMAC Research Reports (Oct. 3, 2005) published the results of a check of MBA alumni. Of the African Americans who responded to the check, 209 reported their employment status after scaling as tone-employed or a small business proprietor. Of the whites who responded to the check, 356 reported their employment status after scaling as tone-employed or a small business proprietor. Use this information to answer the exploration question.
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