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.

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im sorry me and my friends posted the same question thinking someone will respond earlier.since you already seen my question why haven't I got a reply?

To find the warranty period in days for a washing machine with an average (mean) life of 6 years and a standard deviation of 2.5 years, we can use the concept of the normal distribution.

The normal distribution is a symmetric bell-shaped curve that represents the distribution of a continuous variable. In this case, we can assume that the average life of a washing machine follows a normal distribution.

The z-score is a measure of how many standard deviations a particular value is from the mean. We can calculate the z-score using the formula:

z = (x - μ) / σ

Where:
- z is the z-score
- x is the value we want to convert to a z-score (in this case, the warranty period)
- μ is the mean of the distribution (6 years)
- σ is the standard deviation of the distribution (2.5 years)

Since we want to find the warranty period in days, we need to convert the average life and standard deviation to days by multiplying them by 365.

μ = 6 years * 365 days/year = 2190 days
σ = 2.5 years * 365 days/year = 912.5 days

Now, we can substitute the values into the z-score formula:

z = (x - 2190) / 912.5

To find the warranty period, we need to find the z-score that corresponds to a given probability. Since the standard normal distribution is used in many statistical tables, we typically want to find the z-score that corresponds to a specific probability, such as finding the z-score for a given confidence level.

Once we have the z-score, we can convert it back to the value of x (the warranty period in days) using the formula:

x = μ + z * σ

Let's say we want to find the warranty period that corresponds to a 95% confidence level, which corresponds to a z-score of approximately 1.96.

x = 2190 + 1.96 * 912.5

Calculating this equation will give us the warranty period in days for the washing machine at a 95% confidence level.