Question

The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 24 minutes and 16 minutes, respectively. [You may find it useful to reference the z table.]

a. Find the probability that a randomly picked assembly takes between 19 and 29 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 45 minutes or below 7 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 = = 24

standard deviation = = 16

a)

P(19 < x <29 ) = P((19-24)/16 ) < (x - ) /  < (29-24) / 16) )

= P( -0.31< z <0.31 )

= P(z <0.31 ) - P(z < -0.31)

= 0.6217 -0.3783

Probability = 0.2434

b)

P(x >45 )orP(x < 7) = 1 - P(x < 45) + P(x < 7)

= 1 - P((x - ) / < (45-24) /16 ) + P((x - ) / < (7-24) / 16)

= 1 - P(z < 1.31) +  P(z <-1.06 )   

= 1 - 0.9049 + 0.1446   

= 0.2397

Proportion = 0.2397