Question

A normal population has a mean of 20.0 and a standard deviation of 4.0.

a. Compute the z value associated with 25.0.
b. What proportion of the population is between 20.0 and 25.0?
c. What proportion of the population is less than 18.0?

Answer 1

a) The z-value associated with 25.0

Z = 1.25

b) proportion of the population is between 20.0 and 25.0 is

Proportion = 0.3944

c) proportion of the population is less than 18.0 is

Proportion = 0.3085

Calculations:

Normal pop has mean of 20.0

standard deviation = 4.0

XNN(20.0, 4.0)

a).

`z=(x-h)/(z)`

`=(25-20)/(4.0) =(5)/(4) =1.25`

Z = 1.25

b).

The proportion between 20 and 25 is P(20 <x<25.0)

`=p((20-20)/(4) < z < (25-0)/(4) )`

`=P(0 < z < 1.25)`

`=P(Z < 1.25)-P(z < 0)`

`=0.8944-0.5000`

P(20 < x < 25)=0.3944

c).

The proportion value is less than 18 when

`P(x < 18)=p((x--4)/(6) < (18-20)/(4)`

`=P(z < (-2)/(4))`

`=P(z < -0.5)`

P(x<18) = 0.3085