The speed at which an automated assembly line produces a product follows a normal distribution, with a mean production time of 32.20 sec and a standard deviation of 1.05 sec.A full production run from this line consists of 20 completed products.What is the probability that a full production run will take less than 32 sec, on average, to finish?
A) 0.4247
B) 0.1977
C) 0.1900
D) 0.5753

Question

Quizplus · Accepted Answer

To find the probability that a full production run will take less than 32 seconds, we need to find the z-score for 32 seconds and then find the corresponding probability from the standard normal distribution table.

z = (32 - 32.20)/1.05 = -0.1905

Looking up the corresponding probability for a z-score of -0.19 in the standard normal distribution table, we get 0.4247.

However, since we want the probability that the full production run will take less than 32 seconds on average, we need to divide this probability by the number of completed products in the run (20):

0.4247/20 = 0.0212

So the final answer is 0.0212, which is closest to option B (0.1977).

The Speed at Which an Automated Assembly Line Produces a Product