Normal Distribution Standardising Scores & Reverse Stats 1 with Liz

Starter Given that Find (a) (b) (c) General Rule:

P(Z > -0.6) has the same area as P(Z < 0.6). z is a Negative Value Example 1: Find P(Z > -0.6). Looking in your chart, there are no negative values listed… To get around this, simply make a quick sketch of the normal distribution curve & find a symmetrical point that is in the table. P(Z > -0.6) has the same area as P(Z < 0.6). P(Z < 0.6) = 0.72575

z is a Negative Value In general: If we are looking for a negative z value, we can find it in the table by looking for the same positive value, but the inequality sign has flipped!

z is a Negative Value Example 2: Find P(Z < -1.4). Look at a sketch & use the new flip rule. This is the same as P(Z > 1.4). Remember, our table only tells us values LESS THAN z, so we need to work out 1 – P(Z < 1.4). 1 – P(Z < 1.4) = 1 – 0.91924 = 0.08076

z is a Negative Value For the situation on example 2, you can either think through the process, or simply memorise the shortcut:

z is Between Two Values General Rule: If z is between two values, such as P(a < Z < b)… It is the same as finding P(Z < b) – P(Z < a)

z is Between Two Values Example 3: Find P (1.0 < Z < 2.0)

Working backwards Sometimes the question will give you the probability and ask you which z value it works for. Example 4: Find z when To work this out, look in the table to find the closest z value that yields 0.99534 as its probability. z is 2.6.

Working backwards Example 5: Find (a) (b)

What if our mean isn’t 0 and variance isn’t 1? In this case, we have to standardise our score using this formula:

Standardising Scores Example 6:

You try!

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