Question

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 374 and a variance of 1,090. A unit is deemed faulty if it scores below 320. Find the probability of a random unit being faulty. Give your answer as a decimal to 2 decimal places.

Answer 1

Answer:

The probability of a random  unit is deemed faulty if it scores below 320.

P( X < 320 ) = 0.0505

Step-by-step explanation:

Explanation:-

Given mean of the Population 'μ' = 374

Variance of the Population σ² = 1090

Standard deviation of the  Population 'σ ' = √1090 = 33.01

Given 'X' be a random variable in normal distribution

$Z = \frac{x -mean}{S.D} = \frac{320-374}{33.01} = -1.636$

Z = - 1.64

The probability of a random  unit is deemed faulty if it scores below 320.

P( X < 320 ) = P( Z < - 1.64 )

                   = 1- p(Z > 1.64)

                   = 1 - ( 0.5 + A(1.64)

                   = 0.5 - 0.4495

                  = 0.0505

The probability of a random  unit is deemed faulty if it scores below 320.

P( X < 320 ) = 0.0505