Question

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 weights 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 %​

Answer 1

a. 0.15%

Explanation:

The Z-score of a 945-lb car is ...

(X -μ)/σ = (945 -3550)/807 ≈ -3.23

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%.

_____

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%.