The scores on a mathematics exam have a mean of 65 and a standard deviation of 7. Find the x-value that corresponds to the z-score 1.645.

Z = (x - mean)/SD

Insert the numerical values and solve for x.

To find the x-value that corresponds to the given z-score, you can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the corresponding x-value, μ is the mean, and σ is the standard deviation.

In this case, the mean (μ) is 65 and the standard deviation (σ) is 7.

Substituting the given values into the formula, we have:

1.645 = (x - 65) / 7

Now, let's solve for x.

Multiply both sides of the equation by 7:

1.645 * 7 = x - 65

11.515 = x - 65

Add 65 to both sides of the equation:

11.515 + 65 = x

76.515 = x

Therefore, the x-value that corresponds to the z-score 1.645 is approximately 76.515.

To find the x-value that corresponds to a given z-score, we can use the formula:

x = μ + (z * σ)

Where:
x is the value we are trying to find,
μ is the mean of the data,
z is the z-score, and
σ is the standard deviation.

In this case, the mean (μ) is given as 65 and the standard deviation (σ) is given as 7. The z-score (z) is given as 1.645.

Plugging these values into the formula, we get:

x = 65 + (1.645 * 7)

Calculating the expression, we find:

x ≈ 65 + 11.515

x ≈ 76.515

Therefore, the x-value that corresponds to the z-score 1.645 is approximately 76.515.