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Textbook Expert
Textbook ExpertVerified Tutor
19 Nov 2021

Given information

In a normal distribution,  and  This tells you that x = –5 is ____ standard deviations to the ____ (right or left) of the mean.

Step-by-step explanation

Step 1.

If  is the normally distributed random variable and,  then the score is

  

The value tells, how many standard deviations the value of  is above (to the right) or below (to the left) the mean,   

When  is positive,  is above or right of the mean, and when  is negative,  is below or left of the mean.

The  score in normal distribution tells us how many standard deviations above or below the mean a particular value is. The negative value of the  score tells us the value is below the mean and the positive value tells us the value is above the mean. The formula for score is

.  

Therefore, using the definition of z-score, the value of  indicates that  is 6 standard deviations to the right of mean.

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