Suppose x has a distribution with a mean of 50 and a standard deviation of 27. Random samples of size n = 36 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has distribution with mean μx = and standard deviation σx = . (b) Find the z value corresponding to x = 41. z = (c) Find P(x < 41). (Round your answer to four decimal places.) P(x < 41) = (d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 41? Explain. No, it would not be unusual because more than 5% of all such samples have means less than 41. No, it would not be unusual because less than 5% of all such samples have means less than 41. Yes, it would be unusual because more than 5% of all such samples have means less than 41. Yes, it would be unusual because less than 5% of all such samples have means less than 41.
a) = 50
= = 27/ = 4.5
b) z = (x - )/()
= (41 - 50)/4.5 = -2
C) P(x < 41)
= P(Z < -2)
= 0.0228
d) Yes, it would be unusual because less than 5% of all such samples have means than 41.
Suppose x has a distribution with a mean of 50 and a standard deviation of 27....
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