Question

The average lifespan of a KoldWerks refrigerator is normally distributed with a mean of 14 years and a standard deviation of 2.5 years. What is the probability that a KoldWerks refrigerator will last longer than 15 years?

Answer 1

To find the probability of a KoldWerks refrigerator lasting more than 15 years, calculate the Z-score using 15 years, then subtract the cumulative probability up to that Z-score from 1. The Z-score can be looked up in a normal distribution table or calculated using a statistical tool.

Step-by-step explanation:

The student's question relates to the normal distribution and probability calculation in statistics. Given that the average lifespan of a KoldWerks refrigerator is normally distributed with a mean of 14 years and a standard deviation of 2.5 years, to calculate the probability that a refrigerator will last longer than 15 years, we need to use the Z-score formula which is Z = (X - mean) / standard deviation. Here, X is 15 years.

First, calculate the Z-score:

Z = (15 - 14) / 2.5 = 0.4

Next, we look up the Z-score in a standard normal distribution table or use a statistical tool to find the probability to the left of Z=0.4, which we then subtract from 1 to find the desired probability:

P(Z > 0.4) = 1 - P(Z < 0.4)

After finding the P(Z < 0.4) using the Z-table or an online calculator, we subtract that value from 1 to get the probability that a KoldWerks refrigerator will last longer than 15 years.