Question

** I need this answered BUT I would like you to explain the answer to me so I can understand it... is there a formula for this ?

Assume that a population of thousands of people whose responses were used to develop an anxiety test had scores that were normally distributed with M = 30 and s = 10. What proportion of people in this population would have anxiety scores within each of the following ranges of scores?

• Below 20.

• Above 30.

• Between 10 and 50.

Answer 1

Solution,

Given that ,

mean = M = 30

standard deviation = s = 10

1) P(x < 20 ) = P[(x - M) / s < ( 20 - 30) / 10 ]

= P(z < -1.00 )

Using z table

= 0.1587

2) 1) P(x > 30 ) = 1 - P[(x - M) / s < ( 30 - 30) / 10 ]

= 1 - P(z < 0.00 )

Using z table

= 1 - 0.5000

= 0.5000

3) P( 10 < x < 50) = P[( 10 - 30 )/ 10 ) < (x - M) /s < ( 50 - 30 ) / 10 ) ]

= P( -2.00 < z < 2.00)

= P(z < 2.00 ) - P(z < -2.00)

Using z table

= 0.9772 - 0.0228

=0.9544