Question

NeverReady batteries has engineered a newer, longer lasting AAA battery. The company claims this battery has an average life span of 17 hours with a standard deviation of 0.7 hours. Your statistics class questions this claim. As a class, you randomly select 30 batteries and find that the sample mean life span is 16.7 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 16.7 hours or less

Answer 1

0.020

Explanation:

Given that,

μ = 17,

σ = 0.7,

x¯ = 16.7 hours

n(number of batteries) = 30

To find,

The probability(e) by using μ\frac{σ}{
`√(n)`} = normal cdf

∵ (E - 99, 16.7 , 17, 0.8/
`√(30)`)

The probability of getting a random sample of 30 batteries = 0.020

Hence, the claim is reasonable as only 2% of batteries are likely to last till 16.7 hours.