To find the number of machine parts that will be rejected, we need to calculate how many standard deviations away from the mean a machine part with diameter greater than or equal to 2 standard deviations away will be.
The formula to calculate the number of standard deviations away from the mean is:
z = (x - μ) / σ
Where:
z = number of standard deviations away from the mean
x = value of the diameter
μ = mean of the diameter distribution
σ = standard deviation of the diameter distribution
In this case, we want to find the number of machine parts with a diameter greater than or equal to 2 standard deviations away from the mean. So we need to calculate:
z = (x - μ) / σ
z = (x - 15.000) / 0.030
z = 2
Now, we need to find the area under the normal distribution curve to the right of z = 2, which represents the proportion of machine parts that will be rejected.
We can use a standard normal distribution table to find this area. Looking up the value of z = 2 in the table, we find that the area to the right of z = 2 is approximately 0.0228.
Finally, to find the number of rejected machine parts, we multiply the proportion by the total number of machine parts:
Number of rejected machine parts = Proportion * Total number of machine parts
Number of rejected machine parts = 0.0228 * 15,000
Number of rejected machine parts ≈ 342
Therefore, the correct answer is not listed among the options provided.