1.The heights of 18 year-old men are approximately normally distributed, with mean 66 inches and standard deviation 5 inches. (a) What is the probability that an 18 year-old man selected at random is between 65 and 67 inches tall? (Use 3 decimal places.) (b) If a random sample of thirteen 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Use 3 decimal places.) 2.The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a standard deviation of 2.7 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Use 3 decimal places.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
1.The heights of 18 year-old men are approximately
(b) If a random sample of thirteen 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Use 3 decimal places.)
(b) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Use 3 decimal places.)
(c) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Use 3 decimal places.)
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X: The height of a randomly selected 18 year-old man .
To find:
the probability that an 18 year-old man selected at random is between 65 and 67 inches tall
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