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Question

Suppose x has a distribution

with a mean of 90 and a standard deviation of 36. Random samples of size n = 64

 are drawn.

(a) Describe the x distribution

 and compute the mean and standard deviation of the distribution. 

x

 has  

---Select---

 

an approximately normal

 

a Poisson

 

an unknown

 

a geometric

 

a binomial

 

a normal

 

 distribution with mean μx =  

 and standard deviation σx =  

 .


(b) Find the z value corresponding to x = 81.

 

z =  

 


(c) Find P(x < 81).

 (Round your answer to four decimal places.) 

P(x < 81) =  

 


(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 81? Explain. 

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