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# Hypothesis testing and Probability problems

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1. A perfectly competitive firm is a price taker. That is, no matter how much the firm produces, it can always sell its product at the current price. In other words, a perfectly competitive firm has no control over price; it simply treats the price of its output as given. Suppose that in a given economic sector, 40% of all the firms are expected to be perfectly competitive. If 15 firms from that sector are randomly selected, then

a. What is the probability that no more than 10 firms are perfectly competitive?
b. What is the probability that at least 6 of the selected firms are perfectly competitive?

2. Earning distribution of United Technology is normal; test the hypothesis that on average the quarterly earning is no more than 1.25 based on the sample of 25 quarters earning results which shows the sample mean 1.15 with the population variance of 0.89