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 ?

see the other post.

541.6 To find the lifetime at which 90% of batteries have a lesser lifetime, we need to find the value that corresponds to the 90th percentile of the normal distribution.

To do this, we can use the Z-score formula and the standard normal distribution table.

1. Calculate the Z-score corresponding to the desired percentile. For a normal distribution, the Z-score represents the number of standard deviations a value is above or below the mean.
Z = InvNorm(0.90) [using a normal distribution table or statistical software]

2. Use the Z-score formula to find the actual value:
X = μ + Z * σ

Where:
X = Value at the desired percentile (lifetime in this case)
μ = Mean of the distribution (516 hours)
Z = Z-score corresponding to the desired percentile (found in step 1)
σ = Standard deviation of the distribution (20 hours)

3. Calculate the value:
X = 516 + Z * 20

Now, let's calculate the value at the 90th percentile.

Z = InvNorm(0.90) ~= 1.2816 (using a Z-score table or statistical software)
X = 516 + 1.2816 * 20 ~= 542.632 hours

Therefore, 90% of all 2-volt non-rechargeable batteries in constant use have a lifetime less than approximately 542.632 hours.