The lengths of nails produced in a factory are normally distributed with a mean of 5.095.09 centimeters and a standard deviation of 0.040.04 centimeters. Find the two lengths that separate the top 7%7% and the bottom 7%7%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.

Two diameters that separate the top 7% and the bottom 7% are 5.15 and 5.03 respectively.

Step-by-step explanation:

We are given that the lengths of nails produced in a factory are normally distributed with a mean of 5.09 centimeters and a standard deviation of 0.04 centimeters.

Let X = lengths of nails produced in a factory

So, X ~ N()

The z score probability distribution is given by;

        Z = ~ N(0,1)

where, = population mean

            = standard deviation

Now, we have to find the two lengths that separate the top 7% and the bottom 7%.

         P(X > x) = 0.07

         P( > ) = 0.07

         P(Z > ) = 0.07

So, the critical value of x in z table which separate the top 9% is given as 1.4996, which means;

                    = 1.4996

                     = 5.09 + 0.059984 = 5.15

        P(X < x) = 0.07

         P( < ) = 0.07

         P(Z < ) = 0.07

So, the critical value of x in z table which separate the bottom 9% is given as -1.4996, which means;

                    = -1.4996

                     = 5.09 - 0.059984 = 5.03

Therefore, the two diameters that separate the top 7% and the bottom 7% are 5.15 and 5.03 respectively.

the answer would be a 24

step-by-step explanation:

c=2πr=2·π·3=24