A normal distribution has a mean of 85.7 and a standard deviation of 4.81. Find the data value corresponding to the value of z given. (Enter your answer to four decimal places.)
z = 0.55
Z = (score - mean)/SD
Insert data and solve for score.
To find the data value corresponding to a given value of z, you can use the formula for standardizing a normal distribution:
z = (x - μ) / σ
where z is the standard score, x is the data value, μ is the mean, and σ is the standard deviation.
In this case, you are given the value of z (0.55) and the mean (μ = 85.7) and the standard deviation (σ = 4.81). You need to find the corresponding data value (x).
Rearranging the formula, we get:
x = z * σ + μ
Plugging in the given values, we have:
x = 0.55 * 4.81 + 85.7
Calculating this expression, we find:
x ≈ 88.3555
Therefore, the data value corresponding to z = 0.55 is approximately 88.3555.
To find the data value corresponding to the given value of z, we can use the formula:
x = μ + z * σ
where:
x is the data value we want to find,
μ is the mean of the normal distribution,
z is the value of z-score (from the standard normal distribution),
σ is the standard deviation of the normal distribution.
Given:
μ = 85.7 (mean)
σ = 4.81 (standard deviation)
z = 0.55 (value of z-score)
We can substitute these values into the formula:
x = 85.7 + 0.55 * 4.81
Calculating:
x ≈ 85.7 + 2.6455
x ≈ 88.3455
Therefore, the data value corresponding to z = 0.55 is approximately 88.3455.