For a specific type of machine part being produced, the diameter is normally distributed, with a mean of 15.000 cm and a standar

Question

3 years ago

13

For a specific type of machine part being produced, the diameter is normally distributed, with a mean of 15.000 cm and a standar

d deviation of 0.030 cm. Machine parts with a diameter more than 2 standard deviations away from the mean are rejected. If 15,000 machine parts are manufactured, how many of these will be rejected?
a. 560
b. 680
c. 750
d. 970

Mathematics

2 answers:

Savatey [412] · Answer 1 · 2021-11-12T02:26:37+03:00

Savatey [412]3 years ago

8 0

Answer:

The answer is 750

Step-by-step explanation:

Verizon [17] · Answer 2 · 2021-11-12T01:00:23+03:00

This problem involves Statistics. When you are talking about the number of deviations, you directly refer to what we called the Empirical Rule.

The empirical rule states that 95% of the values will lie within 2 standard deviations of the mean. So 100% - 95% = 5% of the parts will be rejected. So
(0.05)*(15,000) = 750

Therefore, 750 machine parts are rejected. Hope this helps! :D