Math  /  Data & Statistics

QuestionUse the Cumulative Normal Distribution Table to find the zz-score for which the area to its left is 0.690.69. The zz-score for the given area is

Studdy Solution

STEP 1

What is this asking? We need to find the zz-score that has an area of 0.690.69 to its left on the normal distribution curve.
Think of it like finding a specific point on a ruler where 69%69\% of the ruler is to the left of that point! Watch out! Make sure you're looking at the *left* side area in the table, not the right side or the area between the mean and zz.

STEP 2

1. Find the closest probability.
2. Find the corresponding zz-score.

STEP 3

Alright, let's **dive** into the Cumulative Normal Distribution Table!
We're on a **treasure hunt** to find the probability that's *closest* to 0.690.69.
Remember, this table shows us the area to the *left* of a given zz-score, which is exactly what we need!

STEP 4

Scanning through the table, we see a bunch of numbers.
Keep your **eyes peeled** for 0.690.69.
We might not find the *exact* value, but that's okay!
We'll find the closest one we can.

STEP 5

Look! We find 0.69150.6915, which is super close to our target of 0.690.69.
It's just a tiny bit bigger, but it's the best match we've got!

STEP 6

Now that we've found our **magic probability**, 0.69150.6915, let's **unlock** its corresponding zz-score.
The table is organized like a grid, so we'll use our **detective skills** to find the matching row and column.

STEP 7

The row value corresponding to 0.69150.6915 is 0.50.5.
The column value is 0.000.00.

STEP 8

To get the zz-score, we simply **combine** the row and column values: 0.5+0.00=0.500.5 + 0.00 = 0.50.
So, our **target** zz-score is 0.500.50!

STEP 9

The zz-score for which the area to its left is 0.690.69 is approximately 0.500.50.

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