A manufacturing company measures the weight of boxes before shipping them to customers. If the box weights have a population mean of 90 lb and a standard deviation of 24 lb, what is the probability that the average weight of a sample of 36 boxes will exceed 94 lb?

Question

Middle School

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Answer :

**QUESTION 6** Read the extract below and answer the questions that follow.

roundadworthy roundadworthy · Answer 1 · 2025-01-03T21:24:19-05:00

Answer:

The probability that the average weight of the boxes will exceed 94 pounds is 43.25%

Step-by-step explanation:

1. Let's review the information provided to answer the question correctly:

Mean of the population of box weights = 90 pounds

Standard deviation of the population of box weights = 24 pounds

Sample size = 36 boxes

2. What is the probability that the average weight of the boxes will exceed 94 lb?

For answering this question, we will use the z-scores table.

For using the correct z-score, we should use the correct standard deviation. In this case, we have that:

94 - 90 = 4 pounds above the mean.

4 pounds are 4/24 of the standard deviation,

therefore, simplifying:

4/24 = 1/6 = 0.1666......and we'll round to 0.17

z-score is 0.17 because 4 pounds is 1/6 of the standard deviation (24).

The probability of a z-score is 0.5675, but in this case we're asked by a weight over 94 pounds, not under 94 pounds, thus:

1 - 0.5675 = 0.4325

The probability that the average weight of the boxes will exceed 94 pounds is 43.25%