A Normal distribution has a mean of 500 and a standard deviation of 50.A manager wants to simulate two values from this distribution,and has drawn these random numbers: -0.60 and +1.40.Respectively,the two values are:
A) 640 and 440.
B) 470 and 570.
C) 570 and 470.
D) 440 and 640.
E) none of the choices are correct.

Question

Quizplus · Accepted Answer

To simulate a value from a normal distribution, we use the formula:

X = μ + σZ

Where X is the simulated value, μ is the mean of the normal distribution, σ is the standard deviation of the normal distribution, and Z is a standard normal random variable (i.e., a random variable with a mean of 0 and a standard deviation of 1).

For the first value, we have:

X = 500 + 50(-0.6) = 470

For the second value, we have:

X = 500 + 50(1.4) = 570

Therefore, the two values are 470 and 570, which corresponds to choice B.

A Normal Distribution Has a Mean of 500 and a Standard