The top-selling Red and Voss tire is rated 70000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed with a mean of 71200 miles and a standard deviation of 1000 miles.

Question

The top-selling Red and Voss tire is rated 70000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed with a mean of 71200 miles and a standard deviation of 1000 miles.

Express your answers rounded correctly to the thousandths place.

A. What is the probability that the tire wears out before 70000 miles?

B. What is the probability that a tire lasts more than 70800 miles?

Answer 1

http://davidmlane.com/hyperstat/z_table.html

Answer 2

Thank you SO much!

Answer 3

You are welcome.

Answer 4

To calculate the probabilities, we can use the concept of the standard normal distribution. We will convert our given values into z-scores and then use a standard normal distribution table or calculator.

A. To find the probability that the tire wears out before 70000 miles, we need to find the area under the standard normal curve to the left of the z-score corresponding to 70000 miles.

First, we need to convert the given value of 70000 miles into a z-score using the formula: z = (X - mean) / standard deviation

Here, X = 70000 miles, mean = 71200 miles, and standard deviation = 1000 miles.

z = (70000 - 71200) / 1000
z = -12 / 1000
z = -0.012

Now, we can use a standard normal distribution table or calculator to find the probability associated with the z-score of -0.012.

Let's assume the probability is denoted as P(X < 70000). From the standard normal distribution table or calculator, we find that the corresponding probability is approximately 0.4938.

So, the probability that the tire wears out before 70000 miles is 0.494 (rounded to the thousandths place).

B. To find the probability that a tire lasts more than 70800 miles, we need to find the area under the standard normal curve to the right of the z-score corresponding to 70800 miles.

First, we need to convert the given value of 70800 miles into a z-score using the same formula as before.

z = (70800 - 71200) / 1000
z = -400 / 1000
z = -0.400

Now, we can use the standard normal distribution table or calculator to find the probability associated with the z-score of -0.400.

Let's assume the probability is denoted as P(X > 70800). From the standard normal distribution table or calculator, we find that the corresponding probability is approximately 0.6554.

So, the probability that a tire lasts more than 70800 miles is 0.655 (rounded to the thousandths place).