The diameters of ball bearings are distributed normally. the mean diameter is 125125 millimeters and the variance is 2525. find the probability that the diameter of a selected bearing is greater than 130130 millimeters. round your answer to four decimal places.

probability will be

Explanation:

For the normal distribution curves, it is easier to find probability when the medium of distribution is converted to z table.

For Z conversion the mean will be marked as z=0, z=1 will be marked as the point (mean + variance), z=2 will be marked (mean + variance + variance) and so on. Where as z=-1 will have (mean- variance), z=-2 as (mean - variance-variance).

For the given condition 125125mm will be marked z=0.

z=1 will be for 127650 diameter (125125 + 2525 =  127650)

z=2 will denote the diameter 130175.

z=-1 will denote 122600 (125125-2525).

z=-2 will denote 120075.

So, we find the z equivalent value for the asked diameter and find the probability from the given z table (attached). Z value for diameter 130130 is found to be 1.019 (130130/127650)

Important thing is Z table shows probability for less than the particular z value, so if you want to find a greater than marked probability we have to convert it into less than marked probability.

As net probability always makes 1.

This means that for example:

(Probability for a value greater than 15) + (Probability for a value less than equal to 15) = 1.

Thus in our case:

1 = P(diameter < =  130130) + P(diameter > 130130) {P shows probability}

so, P(d > 130130) = 1 - P(d < = 130130) {d stands for diameter}

Thus value of P is found to be:

P (1.019) = P (1.02) = 0.8461

So, P (d > 130130) = 1 - 0.8461 = 0.1539.