The weights of cars are passing over a bridge and have a mean of 3550 lb and a standard deviation of 807 lbs. Assume that the we
ights of the cars are passing over the bridge are normally distributed. Use the empirical rule to estimate the probability that a randomly-selected car going over the bridge with weight less than 945 pounds. a. .15% b. 2.5% c. 99.85% d. 1.5 %
The empirical rule tells you that about 99.7% of the normal distribution is within 3σ of the mean, so less than 1/2 of 0.3% will be more than 3σ below the mean. The most appropriate of these choices is 0.15%.
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The CDF of a normal distribution changes rapidly in the tails, so the difference between 3σ and 3.23σ is pretty large. The actual probability is nearer 0.062%.
