Question

The weight of a particular type of car follows a normal distribution with a mean weight of 2970 pounds and a standard deviation of 840 pounds.About thirty-two percent of cars of this type weigh below what value?

Answer 1

About 32% of the cars with a mean weight of 2970 pounds and a standard deviation of 840 pounds weigh below 2575 pounds.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

$z = \frac{x-\mu}{\sigma} \\\\x= raw\ score, \mu=mean,\sigma=standard \ deviation$

Given that:

mean (μ) = 2970 pounds, standard deviation (σ) = 840 pounds

From the normal distribution table, The 32% corresponds to a z score of -0.47. Hence:

$z = \frac{x-\mu}{\sigma} \\\\-0.47= \frac{x-2970}{840}\\\\x - 2970=-395\\\\x=2575$

Therefore 32% of the cars is below 2575 pounds.

Find out more at: https://brainly.com/question/15016913