Question

QUESTION 10 10 points Save Answer 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 0.8 hours. Your statistics class questions this claim. 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? (Round to 3 decimal places)

Answer 1

Solution :

Given that ,

mean = $\mu$ = 17

standard deviation = $\sigma$ = 0.8

n = 30

$\mu$_{$\bar x$} = 17

$\sigma$_{$\bar x$} =$\sigma$  / $\sqrt$ n = 0.8/ $\sqrt$ 30=0.15

P($\bar x$ < 16.7) = P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (16.7-17) / 0.15]

= P(z <-2 )

Using z table

= 0.0228