00:01
Hey there, welcome to numerate.
00:03
We are asked to find the following probabilities here, knowing that we have a sample size of 16, a population being that equals 1 ,000, and a standard deviation that equals 200.
00:19
So let's start with the probability that x bar is greater than 1 ,070.
00:27
So for this here, we will be setting up our z score.
00:30
Equation taken our 1 ,070, subtracted to our mean, divided by our standard deviation, divided by the square root of our sample size 16.
00:44
Hence, we'll get a z score here, equaling around.
00:49
So let's see what we get.
00:52
1 ,216, we get 1 .4.
00:57
Hence, we can use this probability to find our z score to find our z score, find our probability through a normal distribution table given us 0 .08 07 or we could round this to 08...