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% 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

d. 16.6 and 21.4

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95.44% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 19

Standard deviation = 1.2

About 95.44% of the batteries failed between what two values?

Within 2 standard deviations of the mean

19 - 2*1.2 = 16.6

19 + 2*1.2 = 21.4

So the correct answer is:

d. 16.6 and 21.4

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.