Science scores for high school seniors in the United States are normally distributed with a mean of 60 and a standard deviation of 15. Students scoring in the top 3% are eligible for a special prize consisting of a laptop and $5,000. What is the approximate cutoff score a student must get in order to receive the prize?

As manager of kids skids, meghan wants to develop her relationship management skills. in order to do this, she learns how to

At cooly cola, we are testing the appeal of our new diet one cola. in a taste test of 250 randomly chosen cola drinkers, 200 consumers preferred diet one cola to the leading brand. assuming that the sample were large enough, the large-sample 95% confidence interval for the population proportion of cola drinkers that prefer diet one cola would be:

Suppose that two firms produce differentiated products and compete in prices. as in class, the two firms are located at two ends of a line one mile apart. consumers are evenly distributed along the line. the firms have identical marginal cost, $60. firm b produces a product with value $110 to consumers. firm a (located at 0 on the unit line) produces a higher quality product with value $120 to consumers. the cost of travel are directly related to the distance a consumer travels to purchase a good. if a consumerhas to travel a mile to purchase a good, the incur a cost of $20. if they have to travel x fraction of a mile, they incur a cost of $20x. (a) write down the expressions for how much a consumer at location d would value the products sold by firms a and b, if they set prices p_{a} and p_{b} ? (b) based on your expressions in (a), how much will be demanded from each firm if prices p_{a} and p_{b} are set? (c) what are the nash equilibrium prices?