Question

A set of wrist watch prices are normally distributed with a mean of [76] dollars and a standard deviation of [10] dollars. What is the probability that a randomly selected wrist watch costs more than [80] dollars?

Answer 1

To find the probability that a randomly selected wrist watch costs more than $80, calculate the z-score and find the corresponding area under the standard normal distribution curve.

Step-by-step explanation:

To find the probability that a randomly selected wrist watch costs more than $80, we need to standardize the value using the properties of the normal distribution.

Step 1: Calculate the z-score using the formula: z = (x - mean) / standard deviation

z = ($80 - $76) / $10 = 0.4

Step 2: Look up the corresponding area under the standard normal distribution curve for a z-score of 0.4. This can be done using a Z-table or a calculator. The area to the left of a z-score of 0.4 is approximately 0.6554.

Step 3: Subtract the area to the left from 1 to find the probability that a randomly selected wrist watch costs more than $80.

Probability = 1 - 0.6554 = 0.3446, or 34.46%.