Question

Standard deviation 16.11

Mean 51.24

Assuming the above data were normally distributed, what percent of scores are equal to or less than each of the following scores: Round to two decimal places.

a. 84.5

b. 21,4

c. 24.1

Answer 1

Solution:

Given that,

= 51.24

= 16.11

a ) ( x   84.5 )

=p ( x - /)   ( 84.5 - 51.24 / 16.11 )

= p( z   33 .26 / 16.11 )

= p ( z 2..06 )   

Using z table

= 0.9803

Probability = 0.9803 = 98.03%

b ) ( x   21.4 )

=p ( x - /)   ( 21.4 - 51.24 / 16.11 )

= p( z   - 29.84 / 16.11 )

= p ( z - 1.85 )   

Using z table

= 0.0322

Probability = 0.0322 = 3.22%

c ) ( x   24.1 )

=p ( x - /)   ( 24.1 - 51.24 / 16.11 )

= p( z   -27.14 / 16.11 )

= p ( z - 1.68 )   

Using z table

= 0.0465

Probability = 0.0465 = 4.65%