An engineering firm offers testing for electrical products C

An engineering firm offers testing for electrical products. Currently they are testing a type of compact portable music player. They randomly select a number of the music player and conduct a series of tests and compute an overall score for each unit based upon the results of the testing routine. They determine that the test scores are normally distributed with a mean of 343 and a variance of 1,860. A unit is deemed faulty if it scores below 270. Find the probability of a random unit being faulty. You may find this standard normal table useful. Give your answer as a decimal to 2 decimal places. Probability =

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    270      
u = mean =    343      
          
s = standard deviation =    43.12771731      
          
Thus,          
          
z = (x - u) / s =    -1.69264697      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   -1.69264697   ) =    0.045261342 OR 0.05 [ANSWER]