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The problem asks to find the data value corresponding to a given **z-score** for a normal distribution with a mean of 59.3 and a standard deviation of 2.27, for \( z = 1.51 \).

The formula to convert a **z-score** into a data value (X) is:

\[
X = \mu + z \cdot \sigma
\]

where:
- \(\mu\) is the mean,
- \(\sigma\) is the standard deviation,
- \(z\) is the given z-score.

Substituting the values:

\[
X = 59.3 + 1.51 \cdot 2.27
\]

First, calculate \( 1.51 \times 2.27 \):

\[
1.51 \times 2.27 = 3.4277
\]

Now, add this to the mean:

\[
X = 59.3 + 3.4277 = 62.7277

A normal distribution has mean 59.3 and standard deviation 2.27. Find the data value corresponding to the following value of z: z = 1.51.

Learn how to find the data value for a given z-score (z = 1.51) in a normal distribution with a mean of 59.3 and standard deviation of 2.27. Step-by-step solution included, using the formula X = μ + z * σ.

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