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The mean diameter of holes produced by a drilling machine is 4.05mm and the standard deviation of the diameter is 0.0028mm. for 20 holes drilled using this machine. determine , correct to the nearest whole number how many hare likely to have diameters of between
a) 4.048 and 4.0553
assuming they are normaly distributed

Sagot :

Varshamittal029idn

The hole having the diameters likely between 4.048 and 4.0553 is 17.

Maximum value of diameter = 4.05 + 0.0028 = 4.0528

Minimum value of diameter = 4.05 - 0.0028 = 4.0472

So, the diameters of the holes are in AP with common difference

= (2 × 0.0028) / 20 = 0.00028

So, the AP is:

4.0472, 4.04748, 4.04776, 4.04804, …, 0.0.0528

So, the first 3 terms are not included between 4.048 and 4.0553

Hence, the answer is 20 - 3 = 17

Therefore, the hole having the diameters likely between 4.048 and 4.0553 is 17.

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