Question

Assume that round widgets from a manufacturing process have diameters that are normally distributed with mean 175.25 centimeters and standard deviation 2.35 centimeters. The chances that a randomly selected widget has diameter less than 166 centimeters is closest to which of the following

Answer 1

We have given the normal distribution

X: randomly selected widget diameter

We are asked to find P ( X < 166) (we have word less than in the question so we choose sign < )

Now we find the z score for 166

We round z score to 2 decimal place

z = -3.94

We use negative z table to find the left side area of -3.94

Because Z table always given you left side area directly

We look for row headed -3.9 and column headed 0.04

We get the left side area to z score -3.94 = 0.00004

We are asked about The chances that a randomly selected widget That means we have to write the above probability in to fraction

We multiply and divide by 100000 because we have to get rid of the decimal point form the 0.00004

              

Now we simplify fraction i.e we divide numerator and denominator by 4

Final answer :-

1 out of 25000

i.e

I hope this will help you :)