The time (in minutes) that a randomly selected individual waits for an elevator in an office building has a distribution with a mean of 0.5 and a standard deviation of 0.289. (a) Let X be the sample mean waiting time for a random sample of 50 individuals. What are the mean and standard deviation of the sampling distribution of X? (b) Approximate P(0.45 ≤ X ≤ 0.57).
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5. The standard deviation of the sampling distribution of X is equal to the population standard deviation divided by the square root of the sample size, which is: σ/√n = 0.289/√50 ≈ 0.041 Show more…
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The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution μ = 0.5 and σ = 0.289. (a) Let x be the sample mean waiting time for a random sample of 19 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.) μx = σx = (b) Answer Part (a) for a random sample of 40 individuals. (Round your answers to three decimal places.) μx = σx =
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