After numerous studies, it is estimated that the age of college students follows a normal distribution with a mean of 20.7 years and a standard deviation of 1.8 years. A random sample of 16 college...

After numerous studies, it is estimated that the age of college students follows a normal distribution with a mean of 20.7 years and a standard deviation of 1.8 years. A random sample of 16 college students is taken and the sample mean and sample standard deviation are found to be 21.5 years and 2.3 years, respectively.

a.Is the sample average of 21.5 considered an outlier (in other words, what is the chance of getting a sample mean at least as large as 21.5 assuming μ and σ are correct)?

b. The calculated value of the sample standard deviation is larger than σ, is 2.3 years enough larger than 1.8 that the estimate of σ does not seem reasonable? Use probability to support your conclusion

c.No matter what you got for an answer in part b, assume we no longer trust σ = 1.8 to be valid. Calculate the same probability as you did in part a, but this time, assume that σ is unknown.