The life spans of a computer manufacturer’s hard drives are normally distributed, with a mean of 3 years 6 months and a standard deviation of 9 months. What is the probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months? Use the portion of the standard normal table to help answer the question. z Probability 0 point 0 0 0 point 5 0 0 0 0 point 2 3 0 point 5 9 1 0 0 point 3 3 0 point 6 2 9 3 0 point 6 7 0 point 7 4 8 6 1 point 0 0 0 point 8 4 1 3 1 point 3 3 0 point 9 0 8 2 1 point 6 7 0 point 9 5 2 5 2 point 0 0 0 point 9 7 7 2
Convert the times to months: the mean is 42 months, and the interval is 27 to 39 months. The z-scores are (27 − 42)/9 ≈ −1.67 and (39 − 42)/9 ≈ −0.33. The standard normal probability between those z-scores is about 0.37 − 0.05 = 0.32, or 32 percent, so the correct choice is 32 percent.
AI-written and checked against the verified answer.