The lifetime of a 2- volt non-rechargeable battery in constant use has a normal distribution of 516 hours and a standard deviation of 20 hours. What is the z- score for batteries with lifetimes of 520 hours?
Use z-scores.
Formula:
z = (x - mean)/sd
With your data:
z = (520 - 516)/20
I'll let you finish the calculation.
0.2
To find the Z-score for a specific value, you can use the following formula:
Z = (X - μ) / σ
where:
Z is the Z-score
X is the value you want to find the Z-score for
μ is the mean of the distribution
σ is the standard deviation of the distribution
In this case, you are given that the mean (μ) of the distribution is 516 hours and the standard deviation (σ) is 20 hours. You want to find the Z-score for a battery lifetime of 520 hours, so X = 520.
Plugging in these values into the formula:
Z = (520 - 516) / 20
Z = 4 / 20
Z = 0.2
Therefore, the Z-score for a battery with a lifetime of 520 hours is 0.2.