Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever dogs, each of size nequals 15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain. Choose the correct answer below. A. Yes; the sample size must be over 30 for the sample means to be normally distributed. B. No; the original population is normally distributed, so the sample means will be normally distributed for any sample size. C. No; the samples are collected randomly, so the sample means will be normally distributed for any sample size. D. No; as long as more than 30 samples are collected, the sample means will be normally distributed.

Question

Mathematics

Darryl Miranda

27 April, 19:01

Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever dogs, each of size nequals 15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain. Choose the correct answer below. A. Yes; the sample size must be over 30 for the sample means to be normally distributed. B. No; the original population is normally distributed, so the sample means will be normally distributed for any sample size. C. No; the samples are collected randomly, so the sample means will be normally distributed for any sample size. D. No; as long as more than 30 samples are collected, the sample means will be normally distributed.

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Answers (1)

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Leonard Haynes · Answer 1

B.

Step-by-step explanation:

If the population, in this case, weights of golden retriever dogs, follows a normal distribution, then the sample will too, even if the sample size is lower than 30. You only have to worry about the sample size being too small when a problem doesn't explicitly say the distribution from which the samples are drawn is normally distributed.