Another random sample?

A random sample of size 64 is taken from a normal population with μ=51.4 and σ=6.8. What is the probability that the mean of the sample will


a) exceed 52.9


b) fall between 50.5 and 52.3


c) be less than 50.6?

Another random sample?
a) We want that P(xbar%26gt;52.9) (x bar is an x with a bar on top and represents the sample mean of a random sample, and P stands for probability) sqrt stands for square root in the following





so P(xbar%26gt;52.9)=P(xbar%26gt;(xbar-u)/ (δ/sqrt(n)) or


P(xbar%26gt;(52.9-51.4)/(6.8/sqrt(64))


P(xbar%26gt;1.76)





Now look at your standard normal tables in your book, if it is an upper tail chart then just read it off the chart if it is a lower tail chart then you want 1-P(xbar%26gt;1.76). My chart is a lower tail chart and it says this probability is .9608. The rest of these are similar





b)P((xbar-u1)/ (δ/sqrt(n)) %26lt;xbar%26lt;(xbar-u2)/ (δ/sqrt(n))





c)P(xbar%26lt;(xbar-u2)/ (δ/sqrt(n))








You may have some questions just let me know by posting the questions. Hope this helps.
Reply:As the mean itself is 51.4, it is not possible to exceed 52.9 or be less than 50.6. Hence, the probabilities of a) and c) are 0 and the probability of b) fall between 50.5 and 52.3 is 1. I hope I could explain it clearly.
Reply:exceed 52.9
Reply:no idea.