once again I am not getting this.
assume that the population of heights of male college students is normally distibuted with a mean of 69.09 and standard deviation of 4.71. A random sample of 92 heights is obtained. find the mean and standard error of the x distribution.
find P(x>68.5)
SEm = SD/√n
Best guess at the mean is the population mean.
Z = (score-mean)/SEm
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (P) related to the Z score.
To find the mean and standard error of the x distribution, we first need to calculate the mean and standard deviation of the sample.
The mean of the x distribution (also known as the sample mean) is equal to the mean of the population, which is given as 69.09.
The standard error of the x distribution represents the variability of the sample mean and is calculated using the formula:
standard error = standard deviation / sqrt(sample size)
Given that the standard deviation of the population is 4.71 and the sample size is 92, we can calculate the standard error as follows:
standard error = 4.71 / sqrt(92) ≈ 0.4927
So, the mean of the x distribution is 69.09 and the standard error is approximately 0.4927.
To find P(x > 68.5), we need to calculate the z-score associated with the value 68.5 and then find the corresponding probability in the standard normal distribution.
The z-score can be calculated using the formula:
z = (x - mean) / standard deviation
In this case, the mean is 69.09 and the standard deviation is 4.71. Plugging in these values along with x = 68.5, we get:
z = (68.5 - 69.09) / 4.71 ≈ -0.125
Once we have the z-score, we can use a standard normal distribution table or a calculator to find the probability associated with this z-score.
For P(x > 68.5), we need to find the probability to the right of the z-score -0.125. When looking up the z-score in a standard normal distribution table, we need to find the area to the left of the z-score and subtract it from 1.
Using a standard normal distribution table or a calculator, we find that the area to the left of z = -0.125 is approximately 0.4503. Therefore, the probability P(x > 68.5) is approximately 1 - 0.4503 = 0.5497, or 54.97%.