standard deviation

Question

 for a normal distribution with a mean of 80 and a standard deviation of 20. a. what percent values are between 40 and 120, b. what percent of values are less than 100 c. waht percnet of values between 40 and 80 d. what percent of values are between 20 and 100

Answer 1

For this problem, you can use the 68-95-99.7 Rule, which states that 68% of values are within one standard deviation of the mean, 95% are within two standard deviations, and 99.7% are within three standard deviations.

 

This means that:

 

68% of values are between 80 - 20 = 60 and 80 + 20 = 100

95% of values are between 80 - 2(20) = 40 and 80 + 2(20) = 120 (PART A)

99.7% of values are between 80 - 3(20) = 20 and 80 + 3(20) = 140

 

 

 

Also, remember that exactly 50% of values are below the mean and exactly 50% of values are above it. In fact, that means that:

 

68/2 = 34% of values are between 60 and 80

34% of values are between 80 and 100 (PARTS B AND D)

95/2 = 47.5% of values are between 40 and 80 (PART C)

47.5% of values are between 80 and 120

99.7/2 = 49.85% of values are between 20 and 80 (PART D)

49.85% of values are between 80 and 140

 

 

 

 

(a)

 

From the first part of our thinking, 95% of values are between 40 and 120.

 

 

(b)

 

We know that 50% of values are less than 80. We also know that, from the second part of our thinking, 34% of values are between 80 and 100. So, 50% + 34% = 84% of values are less than 100.

 

 

(c)

 

From the second part of our thinking, 47.5% of values are between 40 and 80.

 

 

(d)

 

From the second part of our thinking, 49.85% of values are between 20 and 80. Also from the second part of our thinking, 34% of values are between 80 and 100. So, 49.85% + 34% = 83.85% of values are between 20 and 100.