Normal: P(X > 70), mean 60, sd 10 Step by Step

Step by step

The question

Question: X is normal, with mean 60 and SD 10: what is the probability that X is more than 70?

P(X > 70): μ = 60, σ = 10

μ is the mean.

σ is the standard deviation, the SD.

μ = the mean, σ = the SD

1 Find z

z counts how many SDs x is from the mean: x minus the mean, over the SD.

z = x − μσ

70 minus 60 is 10.

Divided by 10, that is 1.

z = 70 − 6010 = 1010 = 1

2 Draw and shade

The bell: the mean, 60, in the middle.

70 is right of it.

We want X more than 70.

We shade that part.

3 Read the table

The z-table gives the area to the left of z.

Row 1.0, column .00.

For z = 1: the row 1.0 and the column .00 meet at 0.8413.

4 The area we want

Careful!

0.8413 is the area to the left.

We want the right side.

Careful: not 0.8413 ✗

The whole bell is 1.

The right side is 1 minus the left: 1 minus 0.8413 is 0.1587.

P(X > 70) = 1 − 0.8413 = 0.1587

5 Check

Let's check another way.

The bell is the same on both sides.

So the area right of 1 is the area left of −1.

right of 1 = left of −1

The table at −1 gives 0.1587.

The same!

So it is right!

table at −1: 0.1587

Let's look back.

First: find z.

Then: draw and shade.

Then: read the table.

Then: the area we want.

Last: check.

Answer