# Calculating probability of a sample mean [closed]

I'm in an intro to stats class right now, and have absolutely no idea what's going on. How would I solve the following problem using R?

"Let x be a continuous random variable that has a normal distribution with a mean of 71 and a standard deviation of 15. Assuming n/N is less than or equal to 0.05, find the probability that the sample mean, x-bar, for a random sample of 24 taken from this population will be between 68.1 and 78.3"

I'm really struggling on this one and I still have to get through other problems in the same format. Any help would be greatly appreciated! If it helps, my professor has been using pnorm and qnorm a lot, I'm not sure if either of those are applicable to this problem though.

Before anyone comments berating me to just go see my professor for help, the office hours directly conflict with my work schedule, and yes, the test is in 2 days~ sorry this is one of my lower priority classes.

## closed as off-topic by Glen_b♦Apr 13 '17 at 1:47

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Self-study questions (including textbook exercises, old exam papers, and homework) that seek to understand the concepts are welcome, but those that demand a solution need to indicate clearly at what step help or advice are needed. For help writing a good self-study question, please visit the meta pages." – Glen_b
If this question can be reworded to fit the rules in the help center, please edit the question.

• Please see the help center on homework-style questions, and the self-study guidelines. You either need to ask a much more specific question about the particular difficulties you have, or show an attempt about which some guidance might be offered. – Glen_b Apr 13 '17 at 1:47

## 1 Answer

n/N < 0.05 suggests that the professor wants you to ignore the finite-population correction. Therefore, you need to find the distribution of the sample mean when $n=24$ assuming the population is infinite (i.e., the "usual case"). You can then convert this distribution to the standard normal and look up the probability that the sample mean is located between 68.1 and 78.3.

Hint: if the data are normally distributed, then what is the distribution of the sample mean?

• From the OPs question I had no idea what n/N meant. But taking n to be the sample size and N the size of a finite population is as good a guess as any. I guess in this case n=24. that would make the population size at least 24*20=480. Also keep in mind that when the normal distribution is used you standardize to N(0,1). But the standard deviation for the population has not yet been specified. – Michael Chernick Apr 12 '17 at 20:25
• @MichaelChernick thanks for the edits. As for the population standard deviation, the OP included the following in the first line of the second paragraph: "Let x be a continuous random variable that has a normal distribution with a mean of 71 and a standard deviation of 15", so the population standard deviation is 15 with mean 71. This should be sufficient for the OP to derive the distribution of the sample mean and get the probability. – user145807 Apr 13 '17 at 13:09
• I agree @Bey and that is why I gave your answer an upvote. We provided the needed hints for a self-study question. – Michael Chernick Apr 13 '17 at 13:21