Question

The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 17 minutes and 9 minutes, respectively. [You may find it useful to reference the z table.] a. Find the probability that a randomly picked assembly takes between 15 and 22 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 29 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 = = 17

standard deviation = = 9

a)

P(15 < x < 22) = P((15-17)/ 9) < (x - ) /  < (22-17) / 9) )

= P(-0.22 < z < 0.56)

= P(z < 0.56) - P(z < -0.22)

= 0.7123 - 0.4129

= 0.2994

Probability = 0.2994

b)

P(x > 29) + P(x < 7) = (1 - P(x < 29) )+ P(x < 7)

= (1 - P((x - ) / < (29-17) / 9) )+ P((x - ) / < (7-17) / 9)

= (1 - P(z < 1.33)) + P(z < -1.11)

= (1 - 0.9082) + 0.1335   

= 0.0918 + 0.1335

= 0.2253

Proportion = 0.2253