Question

In: Statistics and Probability

Standard deviation 16.11 Mean 51.24 Assuming the above data were normally distributed, what percent of scores...

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

Solutions

Expert Solution

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%


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