Adiamond merchant has a chance to buy one of 4 diamonds and wants to sell it immediately. one costs only $1000, but he has a 90% chance of getting $5000 for it (or not selling it at all). the second costs $10,000, and he has a 60% change of selling it for $25,000 (or not selling it at all). the third costs $20,000, but he has a 50% chance of selling it for $60,000 (or not selling it at all). the last diamond costs $50,000, but he has a 1% chance of selling it for $1,000,000 (or not selling it at all). which diamond gives him the best expected value?

Muscles, a membership-only gym is hoping to open a new branch in a small city in pennsylvania that currently has no fitness centers. according to their research approximately 12,600 residents live within driving distance of the gym. muscles sends out surveys to a sample of 300 randomly selected residents in this area (all of who respond) and finds that 40 residents say they would visit a gym if one was located in their area. based on the past survey research, muscles estimates that approximately 30% of these respondents would actually join the gym if they opened one in the area. based on this information and the results of the sample survey, about how many residents should muscles expect to join its new branch? a) 134 b) 504 c) 1,680 d) 3,780

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Recall that the owner of a local health food store recently started a new ad campaign to attract more business and wants to know if average daily sales have increased. historically average daily sales were approximately $2,700. the upper bound of the 95% range of likely sample means for this one-sided test is approximately $2,843.44. if the owner took a random sample of forty-five days and found that daily average sales were now $2,984, what can she conclude at the 95% confidence level?