A population of values has a normal distribution with 2145...

A population of values has a normal distribution with = 214.5 and = 7.6. If a random sample of size n = 21 is selected, a. Find the probability that a single randomly selected value is greater than 210.2.Round your answer to four decimals P(X>210.2)= b. Find the probability that a sample of size n = 21 is randomly selected with a mean greater than 210.2. Round your answer to four decimals P(M>210.2) =

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00:01 Hey there, welcome to numerate.

00:03 So we're given population values here.

00:07 They are normally distributed with our mean and population standard deviation given.

00:12 We also have a sample size of 21.

00:14 So with that we're finding the probability that the selective value is greater than 8 .8 .7.

00:20 All right, so let's do part a here first.

00:24 So what we're given here is our mean and population standard deviation here.

00:32 So let's write those first.

00:35 So we have our mean as 77 .9 and we have our population standard deviation, which is denoted as sigma here, equals to 44 .9.

01:09 All right.

01:11 And now with this, we have to find probability that greater than 88 .7.

01:20 So basically is the probability that x is greater.

01:25 Later than 88 .7.

01:30 That's what we're basically finding here.

01:33 So in order to find this, we're gonna use our z score equation to calculate our z score and then use that z score to find our probability.

01:42 All right, so let us do that.

01:47 So what we have here is x greater than 88 .7, so our z score equation, our x will be 88 .7, minus our mean, which is 77 .9, divided by our standard deviation.

02:07 Our standard deviation here equals 44 .9.

02:11 All right.

02:19 We're going to calculate our z score here.

02:23 And we'll get a z score of, let's see...

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