It is known that the amount of time it takes to commute from the north end of a particular city to the south varies with mean 77 minutes and standard deviation 13 minutes. The distribution of commute times is also right skewed. A random sample of 35 commute times is selected. (a) Find the mean (in minutes) of the sampling distribution of the mean commute time for a sample of 35 commutes. $\mu_{\bar{x}} = 77$ min (b) Find the standard deviation (in minutes) of the sampling distribution from part (a). (Round your answer to three decimal places.) $\sigma_{\bar{x}} \approx 2.108$ min (c) Describe the shape of the sampling distribution of the mean commute time for a sample of 35 commutes. approximately normal uniform left skewed right skewed
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Step 1: The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution, as long as the sample size is sufficiently large (usually n ≥ 30). Show more…
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