Question

The capacities (in ampere-hours) were measured for a sample of 120 batteries. The average was 178 and the standard deviation was 12. Find a 95% lower confidence bound for the mean capacity of this type of battery. Round the answer to two decimal places. The lower confidence bound is .

Answer 1

Answer: A 95% lower confidence bound for the mean capacity of this type of battery = 175.85

Step-by-step explanation:

Given: The capacities were measured for a sample : n= 120 batteries.

$\overline{x}=178$ and  $\sigma=12$

lower confidence bound= $\overline{x}-z^c\times\dfrac{\sigma}{\sqrt{n}}$

Critical z value for 9%% confidence = 1.96

So,  a 95% lower confidence bound for the mean capacity of this type of battery will be :

$178-(1.96)\dfrac{12}{\sqrt{120}}\\\\=178-(1.96)(1.0954451)\\\\=(1.96)(1.0954451)\approx175.85$

Hence, a 95% lower confidence bound for the mean capacity of this type of battery = 175.85