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Answer :
The mean and standard error of the mean for the sampling distribution when using random samples of size 8 from a population with a given mean and a standard deviation is calculated. The correct answer is option D: 151.00, 7.07.
When taking random samples from a population, the mean of the sampling distribution will be equal to the population mean. In this case, the population mean is given as 151lb. Therefore, the mean of the sampling distribution is also 151lb.
The standard error of the mean (SE) is calculated by dividing the standard deviation of the population by the square root of the sample size. The standard deviation of the population is given as 20lb, and the sample size is 8. Thus, the standard error of the mean can be calculated as:
SE = standard deviation / √sample size
= 20 / √8
≈ 20 / 2.83
≈ 7.07
Therefore, the mean and standard error of the mean for this sampling distribution, when using random samples of size 8, are 151.00 and 7.07 respectively. This corresponds to option D: 151.00, 7.07.
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