Question

X = the number of items produced by an assembly line during an 8-hour shift can be approximated by a normal distribution with mean value 140 and standard deviation 10. What is the approximate probability that the number of items produced is at most 110?

A. 0.0062
B. 0.1587
C. 0.8413
D. 0.9938

Answer 1

The approximate probability that the number of items produced is at most 110 can be found by standardizing the value using the z-score formula and referring to a standard normal distribution table or calculator.

Step-by-step explanation:

To find the approximate probability that the number of items produced is at most 110, we need to standardize the value using the z-score formula. The z-score is calculated as (x - mean) / standard deviation. In this case, the mean is 140 and the standard deviation is 10.

Substituting the values into the formula, we get the z-score as (110 - 140) / 10 = -3. Using a standard normal distribution table or calculator, we can find the cumulative probability associated with this z-score. The probability that the number of items produced is at most 110 is approximately 0.0013, which is closest to option A, 0.0062.