X~N(570, 103). Find the zscore corresponding to an observation of 470.
A. 0.97  

B. 0.97  

C. 0.64  

D. 0.64 
Answer
General guidance
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 zscore by the transformation,
Stepbystep
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 zscore corresponding to the value 470 can be calculated as:
The zscore corresponding to the value 470 is .
The zscore is obtained as for the value 470 when the random variable X follows normal distribution with mean 570 and standard deviation 103.
Answer
The zscore corresponding to the value 470 is .
Answer only
The zscore corresponding to the value 470 is .