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).

$z=\frac{x-h}{z}$

$=\frac{25-20}{4.0} =\frac{5}{4} =1.25$

Z = 1.25

b).

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

$=p(\frac{20-20}{4} < z < \frac{25-0}{4} )$

$=P(0 < z < 1.25)$

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

$=0.8944-0.5000$

P(20 < x < 25)=0.3944

c).

The proportion value is less than 18 when

$P(x < 18)=p(\frac{x--4}{6} < \frac{18-20}{4}$

$=P(z < \frac{-2}{4})$

$=P(z < -0.5)$

P(x<18) = 0.3085