Question

The weight of a tool manufactured by a tool maker follows a normal distribution with a...

The weight of a tool manufactured by a tool maker follows a normal distribution with a mean of 8kg and a standard deviation of 1.5kg.

For quality control, the Production manager was rejecting any manufactured tool weighing under 6.5 kg. Calculate the approximate percentage of rejected tools.

A.

10%
B.

16%
C.

20%
D.

25%
E.

13%
Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Solution:

Given, X follows Normal distribution with,

   = 8

= 1.5  

Now ,

P(X < 6.5)

= P[(X - )/ <  (6.5 - )/]

= P[Z <  (6.5 - 8)/1.5]

= P[Z < -1.00]

= 0.1587 ... ( use z table)

= 15.87%

= 16% nearly

Answer : 16%

  

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