Math  /  Data & Statistics

QuestionA sample of size 23 will be drawn from a population with mean 6 and standard deviation 5 . (a) Is it appropriate to use the normal distribution to find probabilities for xˉ\bar{x} ? (b) If appropriate find the probability that xˉ\bar{x} will be greater than 4. (c) If appropriate find the 20th 20^{\text {th }} percentile of xˉ\bar{x}. It is appropriate to use the normal distribution to find probabilities for xˉ\bar{x}. The probability that xˉ\bar{x} will be greater than 4 is \square The 20th 20^{\text {th }} percentile of xˉ\bar{x} is \square. It is not appropriate to use the normal distribution to find probabilities for xˉ\bar{x}.

Studdy Solution
(a) Yes, it is appropriate to use the normal distribution. (b) The probability that xˉ\bar{x} will be greater than 4 is approximately **0.973**. (c) The 20th percentile of xˉ\bar{x} is approximately **5.13**.

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