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fredd [130]
2 years ago
10

The lifetime of a 2-volt non-rechargeable battery in constant use has a Normal distribution with a mean of 516 hours and a stand

ard deviation of 20 hours. The proportion of batteries with lifetimes exceeding 520 hours is approximately
A. 0.4207
B. 0.2000
C. 0.5793
Mathematics
1 answer:
Burka [1]2 years ago
8 0

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

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