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 0.8 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,

Answer 1

Answer:

the probability is 0.0202

Step-by-step explanation:

The computation is shown below:

Given that

The Average life span = 17 hours

Standard deviation = 0.8 hours

Sample = 30 batteries

Sample mean = 16.7 hours

Now based on the above information

The probability is

$P (\bar x \leq 16.7) = P (\frac{\bar x - \mu}{(\frac{\sigma }{\sqrt{n} } )} \leq (\frac{16.7 - \mu}{(\frac{\sigma }{\sqrt{n} } )}\\\\= P(z\leq \frac{16.7-17}{\frac{0.8}{\sqrt{30} } } )\\\\= P(\leq -2.05)\\\\= 0.0202$

Hence, the probability is 0.0202