Question

The weights of cars passing over a bridge have a mean of 3,550 pounds and standard deviation of 870 pounds. Assume that the weights of the cars passing over the bridge are normally distributed. find the approximate probability that the weight of a randomly selected car passing over the bridge is between 2,800 and 4,500 pounds

Answer 1

Answer: 0.6672

Step-by-step explanation:

Let x be a random variable representing the weights of the cars. Since they are normally distributed and the population standard deviation is known, we would calculate the z score by applying the formula,

z = (x - μ)/σ

where

x is the sample size

μ = population mean

σ = population standard deviation

We want to find P(2800 < x < 4500)

From the information,

μ = 3550

σ = 870

For x = 2800,

z = (2800 - 3550)/870 = - 0.86

From the normal distribution table, the area under z = - 0.86 is 0.1949

For x = 4500,

z = (4500 - 3550)/870 = 1.09

From the normal distribution table, the area under z = 1.09 is 0.8621

Thus,

P(2800 < x < 4500) = 0.8621 - 0.1949 = 0.6672

the approximate probability that the weight of a randomly selected car passing over the bridge is between 2,800 and 4,500 pounds is 0.6672