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. The proportion of batteries with lifetimes exceeding 520 hours is approximately

A. 0.4207
B. 0.2000
C. 0.5793

Answer 1

Answer: A. 0.4207

Step-by-step explanation:

Given : 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.

i.e. $\mu=516$

$\sigma=20$

Let x denotes the lifetime of a 2-volt non-rechargeable battery in constant use.

Then , the probability of batteries with lifetimes exceeding 520 hours is approximately:-

$P(X>520)=1-P(x\leq520)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{520-516}{20})\\\\=1-P(z\leq0.2)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\ =1-0.5793\ \ [\text{By z-table}]\\\\=0.4207$

Hence, the proportion of batteries with lifetimes exceeding 520 hours is approximately 0.4207.

∴ Correct option is A. 0.4207