Question

The weights of the cars passing over a bridge have a mean 3,550 pounds and standard deviation of 870 pounds. Assume that the weights of the cars passing over the bridge are normally distributed. Use the empirical rule to estimate the percentage of cars over the bridge whose weights are between 1810 and 4420 lbs.

a. 13.5%
b. 81.5%
c. 68%
d. 95%

Answer 1

Mean = 3550

SD = 870

Find P(1810 <x<4420)

z = x -mean / sd

= (1810 - 3550 / 870) < z< (4420 - 3550 / 870)

= -2 <z< 1

Using the -z table -2 = 0.0228 and 1 = 0.8413

Subtract: 0.8413 - 0.0228 = 0.8185 x 100 = 81.85%

Rounding everything may change answer slightly so

The closest one is B 81.5%