Suppose x has a distribution with a mean of 90 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 = 99. z = (c) Find P(x < 99). (Round your answer to four decimal places.) P(x < 99) = (d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 99? Explain. No, it would not be unusual because less than 5% of all such samples have means less than 99. No, it would not be unusual because more than 5% of all such samples have means less than 99. Yes, it would be unusual because less than 5% of all such samples have means less than 99. Yes, it would be unusual because more than 5% of all such samples have means less than 99
a)
= = 90
= / sqrt(n)
= 27 / sqrt(36)
= 4.5
b)
z-score = (x - ) /
= ( 99 -90) / 4.5
= 2
c)
P(X < 99) = P(Z < 2)
= 0.9772 (From Z table)
d)
No, it would not be unusual because more than 5% of all such samples have means less than 99
Get Answers For Free
Most questions answered within 1 hours.