Answer:
<u>The probability that the average weight of the boxes will exceed 94 pounds is 43.25%</u>
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
<u>The probability that the average weight of the boxes will exceed 94 pounds is 43.25%</u>
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