Question

The weights of cars passing over a Bridge have a mean of 3550 lb and a standard deviation of 870 lb. Assume that the weights of the cars passing over the bridge, Lee distributed. Use the empirical rule to estimate the percentage of the cars going over the bridge whose weights are more than 4420 lbs.

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Answer 1

a. 16%

Explanation:

The difference from the mean is ...

(x - µ) = 4420 lb -3550 lb = 870 lb

Then the minimum Z-score of the traffic of interest is ...

(x - µ)/σ = (870 lb)/(870 lb) = 1

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The "empirical rule" tells you that 68% of a normal distribution is within 1 σ (Z = ±1) of the mean. If 68% is inside that range, then the remaining 32% is outside that range. The normal distribution is symmetrical about the mean, so half that quantity is below Z = -1, and the other half, 16%, is above Z=1.

About 16% of the cars have weights more than 4420 pounds.