Question

Delta makes 12-volt car batteries. these batteries are known to be normally distributed with a mean of 45 months and a standard deviation of 8 months. out of a sample of 150 delta car batteries, what is the probability that the mean of the sample is between 44 months and 46.5 months?

Answer 1

To find the probability that the mean of the sample is between 44 months and 46.5 months, calculate the z-scores for both values, use a standard normal distribution table or calculator to find the probabilities, and subtract the lower probability from the higher probability.

Step-by-step explanation:

To find the probability that the mean of the sample is between 44 months and 46.5 months, we need to calculate the z-scores for both values and use the standard normal distribution.

First, calculate the z-score for 44 months:

z = (44 - 45) / (8 / sqrt(150))

z = -0.3536

Next, calculate the z-score for 46.5 months:

z = (46.5 - 45) / (8 / sqrt(150))

z = 0.3536

Using a standard normal distribution table or calculator, find the probability corresponding to each z-score.

For -0.3536, the probability is 0.3622.

For 0.3536, the probability is 0.6378.

Subtract the probability corresponding to the lower z-score from the probability corresponding to the higher z-score to find the probability that the mean of the sample is between 44 months and 46.5 months:

0.6378 - 0.3622 = 0.2756

The probability is 0.2756, or 27.56%.