Question

The per capita energy consumption level​ (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal​ distribution, as shown in the figure. ​(a) What consumption level represents the 7th ​percentile? ​(b) What consumption level represents the 21st ​percentile? ​(c) What consumption level represents the third ​quartile? mean=2302 SD=584.5

Answer 1

Given that,

mean = = 2302

standard deviation = = 584.5

Using standard normal table,

P(Z < z) = 7%

= P(Z < z) = 0.07  

= P(Z <-1.48 ) = 0.07

z = -1.48 Using standard normal table,

Using z-score formula  

x= z * +

x= -1.48*584.5+2302

x= 1436.94

x=1437

(B)

Using standard normal table,

P(Z < z) = 21%

= P(Z < z) = 0.21  

= P(Z <-0.81) = 0.21

z = -0.81 Using standard normal table,

Using z-score formula  

x= z * +

x= -0.81 *584.5+2302

x= 1828.555

x=1829

(C)

The z dist'n Third quartile is,

P(Z < z) = 75%

= P(Z < z) = 0.75  

= P(Z < 0.67 ) = 0.75

z = 0.67

Using z-score formula,

x = z * +

x = 0.67 * 584.5+2302

x = 2693.615

x=2694