Lifetimes of AAA batteries are approximately normally distributed. A manufacturer wants to estimate the standard deviation of the lifetimes of the AAA batteries it produces. A random sample of 23 batteries produced by the manufacturer lasted a mean of 10.3 hours with a standard deviation of 2.4 hours. Find a 95% confidence interval for the population standard deviation of the lifetimes of the batteries produced by the manufacturer.

95% confidence interval for the population standard deviation of the lifetimes of the batteries produced by the manufacturer.

(8.889, 11.7106)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 23

Mean of the sample x⁻ = 10.3

Standard deviation of the sample (s) = 2.4

Level of significance = 0.05

Degrees of freedom = n-1 = 23-1 =22

Step(ii):-

95% confidence interval for the population standard deviation of the lifetimes of the batteries produced by the manufacturer.

(10.3 -  2.8188 (0.50043) , 10.3 + 2.8188(0.50043)

(10.3-1.4106 , 10.3+1.4106)

(8.889, 11.7106)

final answer:-

95% confidence interval for the population standard deviation of the lifetimes of the batteries produced by the manufacturer.

(8.889, 11.7106)

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.