Final answer:
The probability of getting a random sample of 30 batteries in which the sample mean life span is 16.7 hours or less is approximately 1.9%. The class is justified in questioning the company's claim.
Step-by-step explanation:
To determine the probability of getting a random sample of 30 batteries in which the sample mean life span is 16.7 hours or less, we can use the concept of standard deviation and the normal distribution. First, we can calculate the standard error, which is the standard deviation divided by the square root of the sample size. In this case, the standard error is 0.8 / √30 = 0.146, approximately.
Next, we can convert the sample mean of 16.7 hours into a Z-value (standardized score) using the formula Z = (X - μ) / SE. X is the sample mean, μ is the population mean, and SE is the standard error. Plugging in the values, we get Z = (16.7 - 17) / 0.146 = -2.055, approximately.
Finally, we can use a standard normal distribution table or a calculator to find the probability corresponding to the Z-value. The probability of getting a random sample of 30 batteries with a sample mean of 16.7 hours or less is approximately 0.019, or 1.9%. Since this probability is less than 5%, the class is justified in questioning the company's claim.