Question

According to a recent report, replacement times for CD players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years. Find the probability that a randomly selected CD player will have a replacement time of less than 6.0 years.

Answer 1

To find the probability that a randomly selected CD player will have a replacement time of less than 6.0 years, we can use the z-score formula and the standard normal distribution table. The probability is approximately 0.2177 or 21.77%.

Step-by-step explanation:

To find the probability that a randomly selected CD player will have a replacement time of less than 6.0 years, we need to calculate the z-score corresponding to 6.0 years and then use the standard normal distribution table to find the corresponding probability.

The formula to calculate the z-score is: z = (x - mean) / standard deviation. In this case, the mean is 7.1 years and the standard deviation is 1.4 years.

Substituting the values into the formula: z = (6.0 - 7.1) / 1.4 = -0.7857. Now, we can use the z-score table or a calculator to find the probability. In the z-score table, a z-score of -0.7857 corresponds to a probability of approximately 0.2177. Therefore, the probability that a randomly selected CD player will have a replacement time of less than 6.0 years is approximately 0.2177 or 21.77%.