The time required to assemble an electronic component is normally distributed wi

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. Use 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.) Probability 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.) Proportion of assembly times

Explanation / Answer

Mean ( u ) =15
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 < 12) = (12-15)/8
= -3/8 = -0.375
= P ( Z <-0.375) From Standard Normal Table
= 0.35383
P(X < 19) = (19-15)/8
= 4/8 = 0.5
= P ( Z <0.5) From Standard Normal Table
= 0.69146
P(12 < X < 19) = 0.69146-0.35383 = 0.3376                  
b.
To find P( X > a or X < b ) = P ( X > a ) + P( X < b)
P(X < 5) = (5-15)/8
= -10/8= -1.25
= P ( Z <-1.25) From Standard Normal Table
= 0.1056
P(X > 28) = (28-15)/8
= 13/8 = 1.625
= P ( Z >1.625) From Standard Normal Table
= 0.0521
P( X < 5 OR X > 28) = 0.1056+0.0521 = 0.157731                  
proportion of assembly times fall in these unusual categerious 15.7731%

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