The heights of 1000 students are approximately normally distributed with a mean of 174.5 cm and a standard deviation of 6.9 cm. Suppose 20.0 random samples of size 25 students are drawn from this population and the means are recorded to the nearest tenth of a centimeter. Determine a) The standard deviation of the sampling distribution of X-bar (mean). b) The probability of sample means that falls between 172.5 and 175.8 cm. c) The number of sample means that falls between 172.5 and 175.8 cm.
Added by Kathryn W.
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In this case, σ = 6.9 cm and n = 25, so the standard error is 6.9/√25 = 1.38 cm. b) Show more…
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The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. If 200 random samples of size 25 are drawn from this population and the means recorded to the nearest tenth of a centimeter, determine (a) the mean and standard deviation of the sampling distribution of $\bar{X}$; (b) the number of sample means that fall between 172.5 and 175.8 centimeters inclusive; (c) the number of sample means falling below 172.0 centimeters.
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The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. Suppose 200 random samples of size 25 are drawn from this population and the means recorded to the nearest tenth of a centimeter. Determine a) the mean and standard deviation of the sampling distribution, b) the number of sample means that fall between 172.5 and 175.8 centimeters inclusive,
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