Question

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. Ninety percent of all batteries have a lifetime less than
A. 517.28 hours
B. 536. 00 hours
C. 541.60 hours

Answer 1

Answer: C. 541.60 hours

Step-by-step explanation:

Since the lifetime of a 2-volt non-rechargeable battery in constant use has a normal distribution, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = lifetime of the batteries.

µ = mean lifetime

σ = standard deviation

From the information given,

µ = 516 hours

σ = 20 hours

Looking at the normal distribution table, the z score corresponding to ninety percent approximately is 1.28

Therefore,

1.28 = (x - 516)/20

Cross multiplying by 20, it becomes

20 × 1.28 = x - 516

25.6 = x - 516

x = 516 + 25.6

x = 541.6

Therefore, Ninety percent of all batteries have a lifetime less than

541.60 hours