Question

A population of values has a normal distribution with mean of 165.7 and standard deviation of 60.2.

a) Get the z-score for a value of 163. For this problem you use the z score formula z=x−μσz=x-μσ   

b) This z-score tells you how many  the score of 163 is above or below the population mean μμ .

c) Find the probability that a randomly selected value is greater than 163.  

Part 2

A population of values has a normal distribution with mean of 165.7 and standard deviation of 60.2.

You sample 185 values from the population.

a) Get the z-score for a sample mean of 163. For this problem you use the z score formula z=(¯x−μ)√nσz=(x¯-μ)nσ     

b) This z-score tells you how many  the sample mean of 163 is above or below the population mean μμ .

c) Find the probability that a sample mean is greater than 163.  

Enter your numerical answers as numbers accurate to at least 4 decimal places.

Answer 1

X~N (165.7,60.2)

PART 1 :

a) the z-score for a value of 163 be:-

b) This z-score tells that the score of 163 is 0.0449 sd below the population mean .

c) the probability that a randomly selected value is greater than 163 be:-

[ in any blank cell of excel type =NORMSDIST(-0.0449) press enter]

PART 2 :

here, sample size (n) = 185

the sample mean will follow normal distribution with:-

a) the z-score for a sample mean of 163 be:-

b) This z-score tells that the sample mean of 163 is 0.61 sd below the population mean .

c) the probability that a randomly selected sample mean is greater than 163 be:-

[ in any blank cell of excel type =NORMSDIST(-0.61) press enter]

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