Question

The average production per week for Builtrite Furniture is 50,000 units with a standard deviation of 8000 units. What is the probability that a week's production will vary between 58,000 and 62,000 units?

A)2.7%
B)4.0%
C)6.4%
D)9.2%
E)15.8%

Answer 1

To find the probability of producing between 58,000 and 62,000 units at Builtrite Furniture, convert these values to Z-scores and subtract the probability corresponding to Z=1 from that of Z=1.5 using the standard normal distribution. The exact values require using a Z-table or calculator.

Step-by-step explanation:

To calculate the probability that a week's production at Builtrite Furniture will vary between 58,000 and 62,000 units, given that the average production per week is 50,000 units and the standard deviation is 8000 units, we need to use the standard normal distribution (Z-distribution).First, we convert the production numbers 58,000 and 62,000 into Z-scores. This is done by subtracting the mean from the observation and dividing by the standard deviation. The Z-score for 58,000 is (58,000 - 50,000) / 8000 = 1. The Z-score for 62,000 is (62,000 - 50,000) / 8000 = 1.5.

Next, we look up these Z-scores in a standard normal distribution table or use a calculator equipped with standard normal distribution functions to find the probabilities corresponding to these Z-scores.However, without such a table or calculator, we cannot directly provide the exact probability. You would need to use the standard normal distribution to find the probability between these Z-scores.Lastly, the probability of production being between 58,000 and 62,000 units would be the probability at Z=1.5 minus the probability at Z=1.