Question

A sample of 148 values is randomly selected from a population with mean, μ, equal to 46 and standard deviation, σ, equal to 17. (Give your answers correct to one decimal place.)
(a) Determine the interval (smallest value to largest value) within which you would expect 99.7% of such sample means to lie.
Incorrect: Your answer is incorrect. to Incorrect: Your answer is incorrect.

(b) What is the amount of deviation from the mean for a sample mean of 46.7?
Incorrect: Your answer is incorrect.

(c) What is the maximum deviation you have allowed for in your answer to part (a)?
Incorrect: Your answer is incorrect.

Answer 1

http://davidmlane.com/hyperstat/z_table.html

Answer 2

When μ and σ are known, the sample mean (x̄) has normal distribution so the statistic is Z=(x̄-μ)/(σ/sqrt(n)), where n=sample size=148.
(a)
Assuming a symmetrical confidence interval, we have α=0.003/2=0.0015. Looking up a normal probability table, for example:
http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf
we find |Z|=2.96774.
and the confidence interval is given by
μ-Zσ/sqrt(n) ≤ μ ≤ μ+Zσ/sqrt(n)
Substitute σ, μ, and Z to find the confidence interval. Round to one place after the decimal.

(b) deviation = |observed value - actual value |.

(c) The deviation allowed in part (a) is the term that we add/subtract from the mean, namely Zσ/sqrt(n).