A large airline company called Cloudscape Co. monitors customer satisfaction by asking customers to rate their experience as a 1, 2, 3, 4, or 5, where a rating of 1 means "very poor" and 5 means "very good". The customers' ratings have a population mean of =μ4.60, with a population standard deviation of =σ1.94. Suppose that we will take a random sample of =n10 customers' ratings. Let x represent the sample mean of the 10 customers' ratings. Consider the sampling distribution of the sample mean x.Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed.(a)Find μx (the mean of the sampling distribution of the sample mean).=μx (b)Find σx (the standard deviation of the sampling distribution of the sample mean).=σx
Question
A large airline company called Cloudscape Co. monitors customer satisfaction by asking customers to rate their experience as a 1, 2, 3, 4, or 5, where a rating of 1 means "very poor" and 5 means "very good". The customers' ratings have a population mean of =μ4.60, with a population standard deviation of =σ1.94. Suppose that we will take a random sample of =n10 customers' ratings. Let x represent the sample mean of the 10 customers' ratings. Consider the sampling distribution of the sample mean x.Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed.(a)Find μx (the mean of the sampling distribution of the sample mean).=μx (b)Find σx (the standard deviation of the sampling distribution of the sample mean).=σx
Solution
(a) The mean of the sampling distribution of the sample mean (μx) is equal to the population mean (μ). So, μx = μ = 4.60.
(b) The standard deviation of the sampling distribution of the sample mean (σx) is equal to the population standard deviation (σ) divided by the square root of the sample size (n). So, σx = σ/√n = 1.94/√10 = 0.61.
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