. A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 45 months and a standard deviation of 7 months. If the company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)? my answer was 36m is this correct
58 months
53 months
36 months
45 months
49 months
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the Z score = to that proportion. Put values in the above equation and solve for the score.
It doesn't match your choice.
To solve this problem, we need to use the concept of z-scores and the standard normal distribution.
First, we need to find the z-score corresponding to the desired percentage of batteries that would require a full refund. In this case, the company does not want to make refunds for more than 10% of its batteries, so the desired percentage is 10%.
Next, we need to find the z-score value using the standard normal distribution table or a statistical calculator. In the standard normal distribution, the z-score corresponding to a certain percentage is the number of standard deviations away from the mean that corresponds to that percentage.
Using the standard normal distribution table, the z-score corresponding to a percentage of 10% is approximately -1.28. This means that 10% of the batteries will have a lifetime shorter than (mean - 1.28 * standard deviation).
Next, we can calculate the number of months by subtracting the z-score multiplied by the standard deviation from the mean:
Lifetime of batteries = mean - (z-score * standard deviation)
Lifetime of batteries = 45 - (-1.28 * 7)
Lifetime of batteries = 45 + 8.96
Lifetime of batteries ≈ 53 months
Therefore, the correct answer is 53 months.