What if there are more than 2 given in normal distribution?

[soulie]

I have this sample problem for a normal distribution here. I know how to get those in (a) and (b). But I'm a bit puzzled on how to get (c). An explanation would be enough. Thank you!

 

[BigBeachBanana]

View attachment 31683
I have this sample problem for a normal distribution here. I know how to get those in (a) and (b). But I'm a bit puzzled on how to get (c). An explanation would be enough. Thank you!

For c), you're sampling from a normal distribution.
Let [imath]X_1,X_2,\dots,X_{n}[/imath] be i.i.d normally distributed random variables, and [imath]S_n=\frac{X_1+X_2+\dots+X_{n}}{n}[/imath] be the sample average. Then [imath]S_n[/imath] is approximately normal with mean of [imath]\mu[/imath] and the standard error of [imath]\frac{\sigma}{\sqrt{n}}[/imath].

 

[Dr.Peterson]

View attachment 31683
I have this sample problem for a normal distribution here. I know how to get those in (a) and (b). But I'm a bit puzzled on how to get (c). An explanation would be enough. Thank you!

As for "at least 2", you should have learned that that sort of question can commonly be solved by restating "at least 2" as "not 0 or 1". Have you learned about the binomial distribution?