Part 1 A population of values has a normal distribution with μ=227.6μ=227.6 and σ=92.7σ=92.7. You intend to draw a random sample of size n=105n=105.What is the mean of the distribution of sample means?μ¯x= ______What is the standard deviation of the distribution of sample means?(Report answer accurate to 2 decimal places.)σ¯x= ________ Part 2 A population of values has a normal distribution with μ=244 and σ=18.6. You intend to draw a random sample of size n=178.Find the probability that a sample of size n=178 is randomly selected with a mean between 241.8 and 244.4.P(241.8 < M < 244.4) = _______
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Part 1
A population of values has a
What is the
μ¯x= ______
What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
σ¯x= ________
Part 2
A population of values has a normal distribution with μ=244 and σ=18.6. You intend to draw a random sample of size n=178.
Find the probability that a sample of size n=178 is randomly selected with a mean between 241.8 and 244.4.
P(241.8 < M < 244.4) = _______
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