Find the z score corresponding to the given area remember z...

Find the z-score corresponding to the given area. Remember, z is distributed as the standard normal distribution with mean µ = 0 and standard deviation σ = 1. a. The area to the left of z is 15%. b. The area to the right of z is 65%. c. The area to the left of z is 10%. d. The area to the right of z is 5%. e. The area between -z and z is 95%. (Hint: draw a picture and figure out the area to the left of the -z) f. The area between -z and z is 99% USING EXCEL.

Transcript

00:01 We want to find some particular z scores and we want to use excel.

00:06 So i'll start by drawing a normal curve.

00:12 The total area under this curve is one, it's a probability curve.

00:16 It's also symmetric, so area below the mean is 0 .5, above the mean 0 .5.

00:22 We're looking at the standard normal curve, so the mean mu is zero, standard deviation sigma is one, so we've got zero there.

00:31 Okay, so for part we want z such that the area to its left is 15 percent.

00:38 So that means z has to be down here somewhere, so this bit here is 15 percent, 0 .15.

00:45 Now we use the decimal here.

00:48 And how do you get this z score? well, there is a function that takes you from the cumulative area to z.

00:55 It is extremely complicated, we don't do it by hand.

00:59 Luckily, we're using excel.

01:01 On excel, the function that you need is equals invnorm.

01:08 Into this, you're putting a single value, i'll call it a, but it's the cumulative area, that is the area to the left.

01:18 Put this in and it immediately gives you the z score.

01:22 There are similar functions on other software, like on r it's qnorm, on a ti84 it's also invnorm, but it has two extra inputs for mean and standard deviation for a specific distribution.

01:37 On excel, it always gives you the z score, and if it's a specific normal curve, you have to go and do some more work.

01:44 So i'm going to be putting in invnorm 0 .15, and it will tell me that z is minus 0 .104.

02:04 Let me just check, does it say how many decimal places? no, okay, minus 1 .04 to two decimal places.

02:19 Part b, now we want the area to the right 35%.

02:24 Okay, so, oh 65%.

02:28 Oops, i've gone ahead a little bit there.

02:30 So z is here, to the right is 65%, which means to the left is 35%, 0 .35...

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