Question

6. What proportion of scores in a normal distribution have z-scores below z = -1.32? (2 points)

7. What proportion of a normal distribution falls between z = -1.16 and z = 1.16? (2 points)

8. A normal distribution has a mean of µ = 36 with σ = 4. What proportion of the distribution falls between scores of X = 30 and X = 38? (3 points)

Answer 1

solution

(A)P(z < -1.32)

Using z table  

=0.0934

proportion=0.0934

(B)

P( -1.16< Z <1.16 )

= P(Z < 1.16) - P(Z <-1.16 )

Using z table,  

= 0.877-0.123

=0.7540

proportion=0.7540  

(C)

P(30< x <38 ) = P[(30-36) /4 < (x - ) / < (38-36) /4 )]

= P( -1.5< Z <0.5 )

= P(Z <0.5 ) - P(Z <-1.5 )

Using z table   

= 0.6915-0.0668

probability= 0.6247