Suppose that the population mean waist size is 84 cm and that the population standard deviation is 15 cm. How likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm? (Round your answers to four decimal places.)
Referring back to (b), suppose now that the population mean waist size is 82 cm. Now what is the (approximate) probability that the sample mean will be at least 86.3 cm? (Round your answers to four decimal places.)
In light of this calculation, do you think that 82 cm is a reasonable value for μ?
No 82 cm is not a reasonable value for μ since if the population mean waist size is 82 cm, there would be almost no chance of observing a sample mean waist size of 86.3 cm (or higher) in a random sample of 277 men.
Yes 82 cm is a reasonable value for μ since if the population mean waist size is 82 cm, there would be almost no chance of observing a sample mean waist size of 86.3 cm (or higher) in a random sample of 277 men.
No 82 cm is not a reasonable value for μ since if the population mean waist size is 82 cm, there is a reasonably large chance of observing a sample mean waist size of 86.3 cm (or higher) in a random sample of 277 men.
Yes 82 cm is a reasonable value for μ since if the population mean waist size is 82 cm, there is a reasonably large chance of observing a sample mean waist size of 86.3 cm (or higher) in a random sample of 277 men.
Yes 82 cm is a reasonable value for μ since it is almost the same as 50th percentile 81.3.
You may need to use the appropriate table in the Appendix of Tables to answer this question.