X has a normal distribution with a mean of 52 and standard...

X has a normal distribution with a mean of 52 and standard deviation 3.5. (a) Determine P(X being at least 51) (b)Determine P(X more than 53 or less than 50). (c) Determine a value for X so that the probability of X being not less than that value is 0.30. (d) What is the probability of X having a value between 54 and 55? (e) What is the probability of X being at least 51?

Transcript

00:02 Hello, so from the information, we can get a, which is the probability that x is greater than or equal to 51.

00:21 Okay, so this is at least 51.

00:25 And this is a normal distribution to this is greater than or equal to x minus the mean over standard division, which is 3 .5.

00:44 Okay.

00:49 This is going to be equal to negative 2 .86.

00:59 Just a second, this is 0 .286 negative.

01:11 And so this is the same as just a second.

01:16 We can rewrite this as one minus the probability of z less than negative 0 .286.

01:18 And we can write this as one.

01:18 One minus the probability of z less than negative 0 .286.

01:31 Get this result from the z table so we're going to look up 0 .29 from the z table that's negative 0 .29 now probability is going to be 038591 and 0 .38591 so now 1 minus that is going to be equal to 0 .614 .0 9 okay so that's going to be the probability for that now this is the probability that x is more than 53 or less than 50.

02:24 So we're looking at probability of x is more than 53 or x is less than 50.

02:42 So same procedure.

02:45 So you're going to have probability of z greater than 53 minus the mean.

02:52 What is the mean? 52 over standard division 3 .5 plus probability of z less than 50 minus 52 over 3 .5.

03:19 So this one is going to be 1 divided by that.

03:27 0 .286.

03:29 So z greater than 0 .286 plus z is 2 divided 2 .6 plus z is 2 divided by that is going to be negative 0 .57.

03:56 So for this one on the left, it's going to be the same as 1 minus the probability of z less than 0 .286.

04:09 Then we still have this, which is already less than, so we don't have to do anything about that.

04:17 So now we already know the probability of, excuse me, okay, we don't know that.

04:23 Okay, so it's going to be one minus.

04:25 So for 0 .29 positive, that's going to be .6149.

04:38 0 .6149 plus.

04:46 And then we got, this is negative here.

04:50 So negative .57.

04:56 And that's 0 .28434.

05:03 So 0 .28434.

05:09 Okay.

05:11 So our required probability is going to be 1 minus 0 .6.

05:18 1409 plus 0 .28...

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