A music instrument has a lifespan that is normally distributed with a mean of 7 years and a standard deviation of 1 year. If Jason buys this instrument for high school, what is the probability that the instrument will still be working when he finishes college 8.5 years later?

1 answer

To solve this problem, we need to find the probability that the music instrument will last at least 8.5 years. To do this, we need to calculate the z-score associated with the 8.5-year time period.

Using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation, we get:

z = (8.5 - 7) / 1 = 1.5

Next, we need to find the probability associated with this z-score using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find that the probability of a z-score of 1.5 or greater is approximately 0.0668.

Therefore, the probability that the instrument will still be working when Jason finishes college 8.5 years later is approximately 0.0668, or 6.68%.