1. It has been found that times taken by people to complete a particular tax form follow a normal distribution with a mean of 115 minutes and a standard deviation of 45 minutes. (a) (10 pts.) What is the probability that a randomly chosen person takes between 70 and 145 minutes to complete this form? (b) (10 pts.) 12% of all people take more than how many minutes to complete this form? (c) (10 pts.) Two people are chosen at random. What is the probability that at least one of them takes more than an hour to complete this form? (d) (10 pts.) Three people are chosen at random. What is the probability that exactly 1 of them take longer than an hour to complete this form? 2. Candidates for employment at a city fire department are required to take a written aptitude test. Scores on this test are normally distributed with a mean of 280 and a standard deviation of 60. A random sample of 9 test scores was taken. (a) (10 pts.) What is the standard error of the sample mean score? (b) (10 pts.) What is the probability that the sample mean score is less than 270? (c) (10 pts.)What is the probability that the sample mean score is more than 250? 3. A corporation is considering a new issue of convertible bonds. Management believes that the offer terms will be found attractive by 25% of all its current stock-holders. Suppose that this belief is correct. A random sample of 135 current stockholders is taken. (a) (10 pts.) What is the standard error of the sample proportion who finds this offer attractive? (b) (10 pts.) What is the probability that the sample proportion is more than 0.17? (c) (10 pts.)What is the probability that the sample proportion is between 0.18 and 0.23?
Added by Benjamin M.
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We need to find the probability that a randomly chosen person takes between 70 and 145 minutes to complete the form. We can use the z-score formula to standardize these values: z = (x - Ī¼) / Ļ For x = 70, z1 = (70 - 115) / 45 = -1 For x = 145, z2 = (145 - 115) / Show moreā¦
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