The heights of North American women are nor-mally distributed with a mean of 64 inches and a standard deviation of 2 inches. a. b. c. What is the probability that a randomly selected woman is taller than 66 inches? A random sample of four women is selected. What is the probability that the sample mean height is greater than 66 inches? What is the probability that the mean height of a random sample of 100 women is greater than

Complete Question

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a

b

c

Step-by-step explanation:

From the question we are told that

   The  population mean is  

    The standard deviation is  

The probability that a randomly selected woman is taller than 66 inches   is mathematically represented as

Generally

So  

From the z-table  the value of  

 So  

Considering b

 sample mean is  n  =  4  

Generally the standard error of mean is mathematically represented as

=>    

=>    

The probability that the sample mean height is greater than 66 inches    

=>  

=>  

From the z-table  the value of  

=>

Considering b

 sample mean is  n  =  100

Generally the standard error of mean is mathematically represented as

=>    

The probability that the sample mean height is greater than 66 inches

=>  

From the z-table  the value of  

c is the answer

step-by-step explanation: