Question

Assume weights of 10-year-old boys vary according to a Normal distribution with mean μ = 70 pounds and standard deviation σ = 10 pounds. What percentage of this population is greater than 80 pounds?  

Answer 1

(a)

= 70

= 10

To find P(X>80):

Z = (80-70)/10

= 1.00

By Technology, Cumulative Area Under Standard Normal Curve = 0.8413

So,

P(X>80):= 1 - 0.8413 = 0.1587 = 15.87%

So,

Answer is:

15.87%

(b)
= 70

= 10

To find P(X<60):

Z = (60-70)/10

= -1.00

By Technology, Cumulative Area Under Standard Normal Curve = 0.1587

So,

P(X<60) = 0.1587 = 15.87%

So,

Answer is:

15.87%