Question

The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 15 minutes and 8 minutes, respectively.

a) Find the probability that a randomly picked assembly takes between 12 and 19 minutes. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

b) it is unusual for the assembly time to be above 28 minutes or below 5 minutes. What proportion of assembly times fall in these unusual categories? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Answer 1

Solution :

Given that,

mean = = 15

standard deviation = = 8

a ) P (12 < x < 19 )

P ( 12 - 15 / 8) < ( x -  / ) < ( 19 - 15 / 8)

P ( - 3 / 8 < z < 3 / 8 )

P (-0.37 < z < 0.37)

P ( z < 0.37 ) - P ( z < -0.37)

Using z table

= 0.6443 - 0.3557

= 0.2886

Probability = 0.2886

b ) P (x >  28 )

= 1 - P (x < 28 )

= 1 - P ( x -  / ) < ( 28 - 15 / 8)

= 1 - P ( z < 13 / 8 )

= 1 - P ( z < 1.62)

Using z table

= 1 - 0.9474

= 0.0526

P( x < 5 )

P ( x - / ) < ( 5 - 15 / 8)

P ( z < - 10 / 8 )

P ( z < -1.25)

= 0.1056

Probability = 0.0526 + 0.1056 =0.1582

Unusual =0.05 > 0.1582