Answer
0.0023 and Yes (see explantions)
Work Step by Step
We have $\mu=3.7, \sigma=0.6$
If a random sample of 32 people who own CD
players is selected, find the probability that the mean
lifetime of the sample will be less than 3.4 years.
$z(3.4)=\frac{3.4-3.7}{0.6/\sqrt {32}}=-2.83$
The probability below z=-2.83 is 0.0023
If the sample mean is less than 3.4 years, would you consider
that 3.7 years might be incorrect?
According to the Central Limit Theorem, when the sample size is large, the sample mean
should be close to the population mean. In this case, if the sample mean is far away from
the presumed population mean, the original 3.7 years might be incorrect.
