Math Snap

STEP 1

What is this asking?
We need to find the $z$-score that has an area of $0.69$ to its left on the normal distribution curve.
Think of it like finding a specific point on a ruler where $69\%$ 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 $z$.

STEP 2

1. Find the closest probability.
2. Find the corresponding $z$-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 $0.69$.
Remember, this table shows us the area to the left of a given $z$-score, which is exactly what we need!

STEP 4

Scanning through the table, we see a bunch of numbers.
Keep your eyes peeled for $0.69$.
We might not find the exact value, but that's okay!
We'll find the closest one we can.

STEP 5

Look! We find $0.6915$, which is super close to our target of $0.69$.
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, $0.6915$, let's unlock its corresponding $z$-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 $0.6915$ is $0.5$.
The column value is $0.00$.

STEP 8

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

The $z$-score for which the area to its left is $0.69$ is approximately $0.50$.