mean=4,743. standard deviation=68. there is an interval into which approximately 95% of the observations should fall. What is the value of the upper extreme o

Question

i want to understand this question i also want to see the work shown

Answer 1

Actually, we know from observation that 95% of the data in a normal distribution will lie within two standard deviations of the mean.  So it will be greater than the mean minus two standard deviations (4743 -2*68 = 4743-136 = 4607) and less than the mean plus two standard deviations (4743 + 2*68 = 4879).

 

So 95% of the data is between 4607 and 4879. Which is the upper extreme?

 

This is sometimes called the 68-95-99.7 Rule  OR the Empirical Rule.  Empirical means that it has been observed from the data.

 

I hope this helps!

 

Answer 2

Using a z-score table (http://www.z-table.com/), 95% of the observations will occur at less than 1.645 standard deviations above the mean.  The z-score is computed as follows:

 

z = (x-μ)/σ

• z = z-score = number of standard deviations that observation x is from the mean = 1.645
• x = the observed datum
• μ = mean = 4743
• σ = standard deviation = 6.8

 

z = (x-μ)/σ

1.645 = (x-4743)/6.8

 

Solve for x.  Values less than x will include 95% of all observations in the data set.