The life of a blood pressure monitor has a normal distribution with an average of 40 years and a standard deviation of one year. What should the warranty be to replace a malfunctioning monitor with - if the company does not want to replace more than 1% of all the monitor.
Thank you in Advance!
Normal distribution table give μ+2.33σ as the 99% level.
Calculate the warranty period accordingly.
Tell me which brand it is that has 40 years mean life! :)
Try z-scores:
z = (x - mean)/sd
Your data:
2.33 = (x - 40)/1
Solve for x.
Note: 2.33 represents the z-score corresponding to the 1% in your problem.
To determine the warranty period for the blood pressure monitor, we need to find the value that corresponds to the 1% cutoff point of the normal distribution.
Step 1: Calculate the z-score
The z-score represents the number of standard deviations away from the mean a particular value is. We can calculate the z-score using the formula:
z = (x - μ) / σ
Where:
x = desired cutoff point (warranty period)
μ = average (mean) of the distribution (40 years)
σ = standard deviation of the distribution (1 year)
Step 2: Find the z-score corresponding to the desired cutoff point
Since we want to find the warranty period that corresponds to the 1% cutoff point, we need to find the z-score that corresponds to the cumulative probability of 0.01. We can use a standard normal distribution table or a statistical calculator to find this value.
Using a standard normal distribution table, we find that the z-score corresponding to a cumulative probability of 0.01 is approximately -2.33.
Step 3: Solve for the warranty period
Now, we can solve for the warranty period (x) using the z-score formula from Step 1:
-2.33 = (x - 40) / 1
Rearranging the equation, we have:
-2.33 = x - 40
Adding 40 to both sides:
x = -2.33 + 40
x = 37.67
Therefore, the warranty period for the blood pressure monitor should be rounded up to 38 years to ensure that no more than 1% of all monitors need to be replaced.