The equation for the standard normal curve is an exponential equation:
y =
e−x2/2
2π
Evaluate this formula for
x = −4, −3, . . . , 3, 4.
(Round your answers to five decimal places.)
To evaluate the given equation for different values of x, we need to substitute each value of x into the equation and calculate the corresponding y-value. Let's follow these steps:
1. Calculate the constant term: 2π.
2. Substitute the first value, x = -4, into the equation:
y = e^((-(-4)^2)/2) / (2π)
Simplify the exponent: (-(-4)^2) = -16
Calculate the exponential part: e^(-16/2) = e^(-8)
Divide by the constant term: e^(-8) / (2π)
Calculate the final value using a calculator or software, rounding to five decimal places.
3. Repeat the process for each of the remaining x-values (-3, -2, -1, 0, 1, 2, 3, 4), substituting each into the equation and calculating the corresponding y-value.
Here are the calculations for each of the x-values:
For x = -4:
y = 0.000335
For x = -3:
y = 0.004432
For x = -2:
y = 0.053991
For x = -1:
y = 0.241971
For x = 0:
y = 0.398942
For x = 1:
y = 0.241971
For x = 2:
y = 0.053991
For x = 3:
y = 0.004432
For x = 4:
y = 0.000335
So, the rounded values for y when x ranges from -4 to 4 are approximately:
0.00034, 0.00443, 0.05399, 0.24197, 0.39894, 0.24197, 0.05399, 0.00443, 0.00034.