Question

3. Last year, the numbers of calculators produced per day at a certain factory were normally distributed with a mean of 560 calculators and a standard deviation of 12 calculators.
(a) On what percent of the days last year did the factory produce 572 calculators or fewer?

(b) On what percent of the days last year did the factory produce 584 calculators or more?
(c) On what percent of the days last year did the factory produce 548 calculators or fewer?

Answer 1

Given  :  the numbers of calculators produced per day at a certain factory were normally distributed with a mean of 560 calculators and a standard deviation of 12 calculators.

To Find :

(a) On what percent of the days last year did the factory produce 572 calculators or fewer?

(b) On what percent of the days last year did the factory produce 584 calculators or more?

(c) On what percent of the days last year did the factory produce 548 calculators or fewer?

Solution:

Mean = 560

SD = 12

Z score = ( Value - Mean) /SD

factory produce 572 calculators or fewer

Z score = ( 572 - 560 )/ 12  = 1

Z score 1 means 84.13 %  

Hence   84.13 %   of the days last year the factory produced 572 calculators or fewer

584 calculators or more

Z score = ( 584 - 560 )/ 12  = 2

Z score 2 means  97.72 %

Hence 100 - 97.72 = 2.28 %

Hence  2.28 %   of the days last year the factory produced 584 calculators or more

548 calculators or fewer

Z score = ( 548 - 560 )/ 12  =-1

Z score -1 means 15.87 %

Hence   15.87 %   of the days last year the factory produced 548 calculators or fewer

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