Question

NeverReady batteries has engineered a newer, longer lasting AAA battery. The company claims this battery has an average life span of 15 hours with a standard deviation of 0.8 hours.Your statistics class questions this claim. As a class, you randomly select 30 batteries and find that the sample mean life span is 14.7 hours. If the process is working properly, what is the probability of getting a random sample of 30 batteries in which the sample mean lifetime is 14.7 hours or less? Is the company's claim reasonable? (Round your probability to four decimal places.)
The company's claim is not reasonable because the probability that a sample of 30 batteries would have a lifetime of at most 14.7 hours is about
_________?

Answer 1

Answer:

0.0202

Explanation:

μ=15, σ=0.8; n=30

p(x≤ 14.7) = p(Ζ ≤ 14.7-15/0.8÷√30)

p(x≤ 14.7) = p(Ζ ≤ -2.05)

p(x≤ 14.7) = 0.0202

So, the company's claim is not reasonable because the probability that a sample of 30 batteries would have a lifetime of almost 14.7 hours is about 0.0202.