SOLUTION: The weights of a certain population of pregnant women are approximately normally distributed with a mean of 62 kilogram and a standard deviation of 16. Suppose that you select repe
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Question 1203236: The weights of a certain population of pregnant women are approximately normally distributed with a mean of 62 kilogram and a standard deviation of 16. Suppose that you select repeated sample of 16 women from this population and calculate the mean for each sample.
If you were to select a large number of random samples of size 16, what would be the mean of the sample means?
What would be their standard deviation? What is another name for this standard deviation of the sample means?
How does the standard deviation of the sample means compare with the standard deviation of the women weight themselves?
If you were to take all the different sample means and use them to construct a histogram, what would be the shape of their distribution?
What is probability of the means of samples is larger than 60 kg?
What is the probability that 16 women selected at random from this population will have the mean weight between 45 and 75 kilogram and the interpretation of the result. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! he weights of a certain population of pregnant women are approximately normally distributed with a mean of 62 kilogram and a standard deviation of 16. Suppose that you select repeated sample of 16 women from this population and calculate the mean for each sample.
If you were to select a large number of random samples of size 16, what would be the mean of the sample means?
the mean of the sample means would be equal to 62, same as the mean of the population.
What would be their standard deviation? What is another name for this standard deviation of the sample means?
the standard deviation of the sample means is called the standard error.
it is equal to the standard deviation divided by the square root of the sample size.
that would be 16 / sqrt(16) = 4.
How does the standard deviation of the sample means compare with the standard deviation of the women weight themselves?
the standard deviation of the population is not the same as the standard deviation of the standard error.
one is the distribution of the weights of the women themselves.
the other is the distribution of the means of the samples of a certaihn size that are taken.
larger samples more accurately reflect what the population mean is, so they will have a smaller standard error.
that's reflected in the formula for standard error.
If you were to take all the different sample means and use them to construct a histogram, what would be the shape of their distribution?
the distrbution of sample means tends becomes more normal as the sample size gets larger, even when the underlying population that the samples are taken from may not be normal.
What is probability of the means of samples is larger than 60 kg?
z = (x-m)/s
z is the z-score
x is the sample mean
m is the population mean
s is the standard error.
formula becomes z = (60-62)/4 = -.5
probability of getting a z-score greater than that is equal to .6915.
that's the probability that the sample mean will be greater than 60.
What is the probability that 16 women selected at random from this population will have the mean weight between 45 and 75 kilogram and the interpretation of the result.
z-score for 45 = (45 - 62) / 4 = -4.25.
z-score for 75 = (75 - 62) / 4 = 3.25
the probability is the aqrea between those two z-scores.
that would be equal to .99941 which is very close to 100%.
here''s a reference on distribution of sample means.
