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Social SciencePart 1A 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) = _______
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) = _______
Expert Answer
Part 1:
The mean of the distribution of sample means is,
Image Transcriptionclose
- 227.6
Thus, the mean of the distribution of sample means is 227.6.
The standard deviation of the distribution of sample means is,
Image Transcriptionclose
92.7 V105 92.7 10.25 9.04
Thus, the standard deviation of the distribution of sample means is 9.04.
Part 2:
The probability that a sa...
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241.8 244 P| 244.4 244 P(241.8 M <244.4) <Z< 18.6 18.6 V178 V178 -2.2 <Z< 1.39 0.4 = P 1.39 = P(-1.58 < Z < 0.29) =P(Z<0.29)-P(Z <-1.58) 0.61409-0.05705 Use Standard Normal Table 0.55704
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