Question

The lengths of nails produced in a factory are normally distributed with a mean of 6.13 centimeters and a standard deviation of 0.06 centimeters. Find the two lengths that separate the top 7% and the bottom 7%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.

Answer 1

Solution:-

Given that,

mean = = 6.13

standard deviation = = 0.06

Using standard normal table,

this is right tail

P(Z > z) = 7%

= 1 - P(Z < z) = 0.07  

= P(Z < z) = 1 - 0.07

= P(Z < z ) = 0.93

= P(Z <1.48 ) = 0.93  

z = 1.48 ( using z table )

Using z-score formula,

x = z * +

x = 1.48* 0.06+6.13

x = 6.2188   centimeters

x=6.22 rounded