Answer:
The data value corresponding to z = 1.96 in a normal distribution with mean 85.8 and standard deviation 4.83 is approximately 94.2238 (rounded to four decimal places).
Explanation:
To find the data value corresponding to a given value of z, we use the formula:
z = (x - μ) / σ
where z is the standardized value (in standard deviation units), x is the data value we want to find, μ is the mean, and σ is the standard deviation.
Rearranging this formula to solve for x, we get:
x = z * σ + μ
Substituting the given values, we have:
x = z * 4.83 + 85.8
Let's say we want to find the data value corresponding to z = 1.96 (which corresponds to the 97.5th percentile in a standard normal distribution). Then we can plug this value into the formula:
x = 1.96 * 4.83 + 85.8
Simplifying the right-hand side, we get:
x = 94.2238
Therefore, the data value corresponding to z = 1.96 in a normal distribution with mean 85.8 and standard deviation 4.83 is approximately 94.2238 (rounded to four decimal places).