# X~n(2.9. 0.78). find the z-score corresponding to an observation of 1.5.

X~N(570, 103). Find the z-score corresponding to an observation of 470.

A. 0.97
B. -0.97
C. 0.64
D. -0.64

## General guidance

Concepts and reason
The concept of normal distribution is used here to calculate the z-score. The normal distribution is used for finding the probability of the continuous variable when the data are more or less symmetric. The probability for being less than or more than some value can be calculated by calculating the area of the curve to the left of that value. On the basis of the z-score and the standard deviation and mean of the distribution, the value of the random variable can be obtained.

Fundamentals

Consider a continuous random variable which follows normal distribution with mean and standard deviation and it can be represented as. The random variable can be converted to the z-score by the transformation,

## Step-by-step

### Step 1 of 2

The provided information in the question is . Therefore, the distribution of the random variable X is normal and the mean of the distribution is and the standard deviation of the distribution is .

As the distribution of the random variable is provided as , the random variable follows the normal distribution with mean 570 and standard deviation 103.

### Step 2 of 2

The provided observation is 470. Therefore, the z-score corresponding to the value 470 can be calculated as:

The z-score corresponding to the value 470 is .

The z-score is obtained as for the value 470 when the random variable X follows normal distribution with mean 570 and standard deviation 103.