Calculating Probability of Sample Mean Differing from True Mean by 2.5 Minutes

[needhelp83]

The time it takes students to solve a certain math problem has a standard deviation of 18 minutes. A random group of 64 students was selected, and they were asked to solve the math problem.

What is the probability that their sample mean will differ from the true mean by no more than 2.5 minutes?

What exactly do I use to determine this problem. Thanks for any help guys.

 

[Billy Bob]

Central Limit Theorem

$$z=\frac{\bar{x}-\mu}{\sigma/\sqrt{n}}$$

We can give more help if that's not enough.

 

[needhelp83]

$$z=\frac{\bar{x}-\mu}{18/\sqrt{64}}$$

So I don't understand where I would put the 2.5 mins. would go and where I would figure out the population mean.

 

[Billy Bob]

You want $$P(|\bar X-\mu|\le 2.5)$$

Divide both sides of $$|\bar X-\mu|\le 2.5$$ by some number so that you have $$P(|Z|\le \text{some constant})$$

Note that you don't need to know the population mean to do this.

 

[needhelp83]

Any help, anybody? More than happy to figure it out if just given a push in right direction.