Question

The amount of weight on an ACME tractor trailer is known to have a normal distribution with mean 9.5 tons and standard deviation 0.5 tons. What is the probability that the weight on a randomly chosen truck exceeds 10.3 tons?

A) 0.0668
B) 0.3085
C) 0.9332
D) 0.6915

Answer 1

To find the probability that the weight on a randomly chosen truck exceeds 10.3 tons, we need to find the area under the normal distribution curve to the right of 10.3 tons. The probability is approximately 0.9452.

Step-by-step explanation:

To find the probability that the weight on a randomly chosen truck exceeds 10.3 tons, we need to find the area under the normal distribution curve to the right of 10.3 tons. This can be calculated using the standard normal distribution table or by using statistical software, such as a calculator or computer program.

Since the mean is 9.5 tons and the standard deviation is 0.5 tons, we can standardize the value by subtracting the mean and dividing by the standard deviation: z = (10.3 - 9.5) / 0.5 = 1.6.

Using the standard normal distribution table, the area to the right of 1.6 is approximately 0.0548.

However, we want the probability that the weight exceeds 10.3 tons, so we subtract this value from 1: 1 - 0.0548 = 0.9452.

Therefore, the answer is C) 0.9452.