The lifetime of a 2- volt non- rechargeable battery in constant use has a normal distribution with a mean of 516 hours and a standard deviation of 20 hours. What is the z-score for batteries with lifetimes of 600 hours?
Use z-scores.
Formula:
z = (x - mean)/sd
With your data:
z = (600 - 516)/20
I'll let you finish the calculation.
To find the z-score for a given value, we need to use the formula:
z = (x - μ) / σ
where:
- x is the value whose z-score we want to find (600 hours in this case)
- μ is the mean of the distribution (516 hours in this case)
- σ is the standard deviation of the distribution (20 hours in this case)
Let's calculate the z-score using the given values:
z = (600 - 516) / 20
= 84 / 20
= 4.2
Therefore, the z-score for batteries with a lifetime of 600 hours is 4.2.