Question

An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before they failed is 19.0 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.2 hours. About 95.44 percent of the batteries failed between what two values?a. 8.9 and 18.9

b. 12.2 and 14.2
c. 14.1 and 22.1
d. 16.6 and 21.4

Answer 1

option (d) 16.6 and 21.4

Explanation:

Data provided in the question:

The mean life for a particular use before they failed = 19.0 hours

The distribution of the lives approximated a normal distribution

The standard deviation of the distribution = 1.2 hours

To find:

The values between which 95.44 percent of the batteries failed

Now,

In Normal distribution, the approximately 95% ( ≈ 95.44% of all values ) falls within 2 standard deviations of the mean

Therefore,

Upper limit = Mean + 2 × standard deviation

⇒ Upper limit = 19.0 + 2 × 1.2 = 21.4

Lower limit = Mean - 2 × standard deviation

⇒ Lower limit = 19 - 2 × 1.2 = 16.6

Hence,

the answer is option (d) 16.6 and 21.4