A manufacturer is concerned over the diameter of rubber balls being produced. Too large and they don’t work for certain applications. Too small and they are subject to little children accidentally choking on them. If the balls are normally distributed with a mean diameter of 1.45 and a standard deviation of .08, what is the value of c , such that 98% of the balls fall between the limits of 1.45 +/- c?

c = 0.1864

Step-by-step explanation:

To find c, we need to find the z-score where:

P(-z<Z<z) = 98%

Based on the properties of the normal distribution we can said that

P(-z<Z<z) = 98% is equal to:

2*P(Z>z) = 2%    or  P(Z>z)= 1%

So, using the standard normal table, the z score is 2.33

Then, we can calculated the value of c as:

Where s is the standard deviation and z is the z-score. Replacing the values, we get:

c = 2.33*0.08

c = 0.1864

probability for j is 1/4

while

a is 1/6