Part 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) = _______

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Asked Nov 4, 2019
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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) = _______

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Expert Answer

Step 1

Part 1:

The mean of the distribution of sample means is,

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- 227.6

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Step 2

Thus, the mean of the distribution of sample means is 227.6.

The standard deviation of the distribution of sample means is,

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92.7 V105 92.7 10.25 9.04

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Step 3

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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