The probability that a randomly selected patient who visits the emergency room will die within 1 year of the visit is 0. 05. (binomial probability distribution) a) What is the probability that exactly 1 of 10 randomly selected visitors to the ER will die within 1 year? b) What is the probability that fewer than 2 of 25 randomly selected visitors to the ER will die within 1 year? c) What is the probability that at least 2 of 25 randomly selected visitors to the ER will die within 1 year? d) Would it be unusual if more than 3 of 30 randomly selected visitors to the ER died within 1 year?
In a random sample of 1000 visitors to the ER, how many visitors are expected to die within the next year? What is the standard deviation number of deaths? 2. Determine whether the random variable is discrete or continuous. a) The flight time accumulated by a randomly selected Air Force fighter pilot. b) The number of points scored by the Miami Heat in a randomly selected basketball game. 3. Suppose that the talk time on the Apple iPhone is approximately normally distributed with mean 7 hours and standard deviation 0. 8 hour. a) What proportion of the time will a fully charged iPhone last at least 6 hours? ) What is the probability a fully charged iPhone will last less than 5 hours? c) What talk time would represent the cutoff for the top 5% of all talk times? d) Would it be unusual for the phone to last more than 9 hours? Why? 4.
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The waist circumference of males 20 to 29 years old is approximately normally distributed, with mean 92. 5 cm and standard deviation 13. 7 cm. a) Use the normal model to determine the proportion of 20- to 29-year-old males whose waist circumference is less than 100 cm. b) What is the probability that a randomly selected 20- to 29-year-old male has a waist circumference between 80 and 100 cm? ) Determine the waist circumference that represents the middle 90% of all waist circumferences. d) Determine the waist circumference that is at the 10th percentile. 5. In a poll conducted by the Gallup organization, 16% of adult, employed Americans were dissatisfied with the amount of their vacation time.
You conduct a survey of 500 adult, employed Americans. (Normal Approximation of Binomial) a) Approximate the probability that exactly 100 are dissatisfied with their amount of vacation time. b) Approximate the probability that less than 60 are dissatisfied with the amount of their vacation time. . The charge life of a certain lithium ion battery for camcorders is normally distributed, with mean 90 minutes and standard deviation 35 minutes. a) What is the probability that a randomly selected battery of this type lasts more than 100 minutes on a single charge? Is this result unusual? b) Describe the sampling distribution of x, the sample mean charge life for a random sample of 10 such batteries. c) What is the probability that a random sample of 10 such batteries has a mean charge life of more than 100 minutes? Is this result unusual?