Question

Please show your work.

A. If a normal distribution of scores has a mean of 100 and a standard deviation of 10, what percentage of scores would lie below 70? a. 0.13%. b.2.15%. c. 2.28% d. 99.87%

B. What percentage of scores lie between 85 and 100 for a normal distribution with a mean of 100 and a standard deviation of 15? a. +15% b.-15% c.34.13% d. -34.13%

C What percentage of scores lie between 70 and 80 for a normal distribution with the mean of 100 and a standard deviation of 10? a.+27% b.-13% c.-7%. d. 2.15%.

Answer 1

Solution :

Given that ,

mean = = 100

standard deviation = =10

P(x < 70) = P(( x -) / (70-100) / 10)

= P(z < -3)

Using z table

= 0.0013

=0.13%

B.

v

Solution :

Given that ,

mean = = 100

standard deviation = =15

P(85< x < 100) = P[(85-100) /15 < (x -) / < (100-100) / 15)]

= P( -1< Z <0 )

= P(Z <0 ) - P(Z < -1)

Using z table,  

= 0.5000-0.1587

= 0.3413

=34.13%

C.

P(70< x <80 ) = P[(70-100) / 10< (x -) / < (80-100) / 10)]

= P(-3 < Z <-2 )

= P(Z < -2) - P(Z < -3)

Using z table,  

= 0.0228-0.0013

= 0.0215

=2.15%