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.