The time required to assemble an electronic component is nor

The time required to assemble an electronic component is normally distributed with a mean and standard deviation of 16 minutes and 8 minutes, respectively. Use Table 1.

Find the probability that a randomly picked assembly takes between 10 and 20 minutes. (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)

It is unusual for the assembly time to be above 24 minutes or below 6 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.)

Solution

Normal Distribution
Mean ( u ) =16
Standard Deviation ( sd )=8
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 10) = (10-16)/8
= -6/8 = -0.75
= P ( Z <-0.75) From Standard Normal Table
= 0.22663
P(X < 20) = (20-16)/8
= 4/8 = 0.5
= P ( Z <0.5) From Standard Normal Table
= 0.69146
P(10 < X < 20) = 0.69146-0.22663 = 0.4649                  

b)
To find P( X > a or X < b ) = P ( X > a ) + P( X < b)
P(X < 6) = (6-16)/8
= -10/8= -1.25
= P ( Z <-1.25) From Standard Normal Table
= 0.1056
P(X > 24) = (24-16)/8
= 8/8 = 1
= P ( Z >1) From Standard Normal Table
= 0.1587
P( X < 6 OR X > 24) = 0.1056+0.1587 = 0.2643