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?
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%.
To find the probability that the instrument will still be working after 8.5 years, we need to calculate the probability of it lasting more than 8.5 years.
First, convert the problem into a standard normal distribution by subtracting the mean and dividing by the standard deviation:
z = (8.5 - 7) / 1 = 1.5
Next, use a standard normal distribution table or calculator to find the probability associated with the z-score of 1.5. This probability represents the area under the curve to the right of 1.5.
Using the standard normal distribution table or calculator, the probability of z > 1.5 is approximately 0.0668.
Thus, the probability that the instrument will still be working when Jason finishes college is 0.0668 or 6.68%.