Consider a population with a population standard deviation of 10.6. In order to compute an interval estimate for the population mean, a sample of 42 observations is drawn. (You may find it useful to reference the z table.)a. Is the condition that x̄ is normally distributed satisfied?multiple choice 1YesNo
Question
Consider a population with a population standard deviation of 10.6. In order to compute an interval estimate for the population mean, a sample of 42 observations is drawn. (You may find it useful to reference the z table.)a. Is the condition that x̄ is normally distributed satisfied?multiple choice 1YesNo
Solution
Yes, the condition that x̄ is normally distributed is satisfied. This is because the Central Limit Theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30). In this case, the sample size of 42 is greater than 30, so the condition is met.
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