Question

Assume that round widgets from a manufacturing process have diameters that are normally distributed with mean 150.55 centimeters and standard deviation 1.68 centimeters. The chances that a randomly selected widget has diameter greater than 156.5 centimeters is closest to which of the following? O a. 1 out of 500 O b. 1 out of 10,000 O c. 1 out of 5,000 O d. 1 out of 1,000

Answer 1

Solution :

P(x > 156.5) = 1 - P(x < 156.5)

= 1 - P[(x - $\mu$ ) / $\sigma$ < (156.5 - 150.55) / 1.68)

= 1 - P(z < 3.54)

= 1 - 0.9998

= 0.0002

option c.

1 out of 5000