Find warranty period (in days) for a washing machine whos average (mean) life is 6 years and standard deviation of 2.5 years. Assume 365 days in a year.
6 * 365 = 2190 days
2.5 * 365 = 912.5 days
What criterion are they using for the warranty? Mean? Mean + 1 SD? Mean + 2 SD?
To find the warranty period (in days) for a washing machine with an average life of 6 years and a standard deviation of 2.5 years, you can use the concept of z-scores.
The z-score measures the number of standard deviations a particular data point is away from the mean. In this case, we want to find the z-score corresponding to the warranty period.
The formula to calculate the z-score is given by:
z = (x - μ) / σ
Where:
x is the value we want to find the z-score for (warranty period in this case)
μ is the mean of the distribution (average life of the washing machine)
σ is the standard deviation of the distribution
We need to find the z-score for a warranty period of 6 years. Substituting the values into the formula, we get:
z = (6 - 6) / 2.5
Since the warranty period value (6 years) is exactly at the mean, the z-score will be zero. A z-score of zero indicates that the value is at the mean of the distribution.
To convert the z-score into days, we multiply it by the standard deviation and then by the number of days in a year (365):
warranty period (in days) = z * σ * number of days in a year
In this case, the z-score is 0, so the warranty period (in days) would be:
warranty period (in days) = 0 * 2.5 * 365 = 0
Therefore, the warranty period for the washing machine with an average life of 6 years and a standard deviation of 2.5 years would be 0 days.