Suppose x has a distribution with a mean of 80 and a standard deviation of 9. Random samples of size n = 36 are drawn. (a)   Describe the X bar  distribution. *X bar has a Poisson distribution. *X bar has an unknown distribution.      *X bar has an approximately normal distribution.  *X barhas a normal distribution.  *X bar has a binomial distribution.  *X bar has a geometric distribution.   Compute the mean and standard deviation of the distribution. (For each answer, enter a number.)  = mu sub x bar = ___________  = sigma sub x bar = _____________ (b)  Find the z value corresponding to  = 77. (Enter an exact number.) z = _____________ (c)  Find P( < 77). (Enter a number. Round your answer to four decimal places.) P( < 77) = P(x bar < 77) = _____________

Question

Suppose x has a distribution with a mean of 80 and a standard deviation of 9. Random samples of size n = 36 are drawn.

(a)

 

Describe the X bar  distribution.
*X bar has a Poisson distribution.
*X bar has an unknown distribution.     
*X bar has an approximately normal distribution. 
*X barhas a normal distribution. 
*X bar has a binomial distribution. 
*X bar has a geometric distribution.
 
Compute the mean and standard deviation of the distribution. (For each answer, enter a number.)

 = mu sub x bar = ___________

 = sigma sub x bar = _____________

(b)

 Find the z value corresponding to  = 77. (Enter an exact number.)
z = _____________

(c)

 Find P( < 77). (Enter a number. Round your answer to four decimal places.)
P( < 77) = P(x bar < 77) = _____________

(d)

 Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 77? Explain.
*Yes, it would be unusual because less than 5% of all such samples have means less than 77.
*Yes, it would be unusual because more than 5% of all such samples have means less than 77.    
*No, it would not be unusual because less than 5% of all such samples have means less than 77.
*No, it would not be unusual because more than 5% of all such samples have means less than 77.

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