Answer:
2.89% probability that weight for a part made using the new production process is less than 1.61 or greater than 2.53 pounds
Explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:

Find the probability that weight for a part made using the new production process is less than 1.61 or greater than 2.53 pounds
Less than 1.61
This is the pvalue of Z when X = 1.61. So



has a pvalue of 0.0110
Greater than 2.53
1 subtracted by the pvalue of Z when X = 2.53.



has a pvalue of 0.9821
1 - 0.9821 = 0.0179
Less than 1.61 or greater than 2.53 pounds
0.0110 + 0.0179 = 0.0289
2.89% probability that weight for a part made using the new production process is less than 1.61 or greater than 2.53 pounds