The lifetime of a 2-volt non-rechargeable battery in contant use has a normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Ninety percent of all batteries have a lifetime less than ?
http://davidmlane.com/hyperstat/z_table.html
See what happens when you are above the mean by 1.28 standard deviations.
sadas
To find the lifetime at which 90% of all batteries have a lifetime less than, we need to find the z-score or the standard score for this given probability. The z-score can be obtained using the standard normal distribution table or a statistical calculator.
The z-score formula is:
z = (x - μ) / σ
Where:
z = z-score
x = value or lifetime of the battery
μ = mean or average lifetime of the batteries
σ = standard deviation of the lifetime of the batteries
In this case, the mean (μ) is given as 516 hours, the standard deviation (σ) is 20 hours, and the required probability is that 90% (0.90) of all batteries have a lifetime less than x.
To find the z-score from the standard normal distribution table, we need to find the value that corresponds to the 90th percentile (0.90). This is also known as the critical value.
Let's use the cumulative distribution function (CDF) or the inverse normal distribution function on a statistical calculator to find the critical value for 90%:
z_critical = invNorm(0.90)
Using the invNorm function, we can find the z-score corresponding to the 90th percentile. In this case, the z_critical value is approximately 1.28.
Now, we can rearrange the z-score formula to solve for x:
x = z * σ + μ
Substituting the known values:
x = 1.28 * 20 + 516
Calculating:
x ≈ 541.6
Therefore, approximately 541.6 hours is the lifetime at which 90% of all 2-volt non-rechargeable batteries have a lifetime less than.