# Normal curve tail area

## 0. Quick guide - background

In this module:

1. Construct a chart of the normal distribution density function - using area charts (Fig 1.)
2. Compare the tail area color for fine and coarse step sizes (Fig 1.)
3. Perform a visual comparison to the Peltier (2013) version with its XY-area chart combination plus date axis (Fig 1.)

## 1. Normal tail area

Circle numbers refer to image components in figure 1.

### xlf :: combo area - area :: step 0.1

• Worksheet: N(0, 1) #2
• z value: cell U7: -3.5
• Formula: cell V7: =NORM.S.DIST(U7,FALSE)
• z step: 0.1
• Chart type: Combo - Area and Area

The coarse step increment causes the left margin of the blue tail area to slope (1.5 at the base to 1.6 at the peak).

### xlf :: combo area - area :: step 0.01

• Worksheet: N(0, 1) #2
• z value: cell B7: -3.5
• Formula: cell C7: =NORM.S.DIST(B7,FALSE)
• z step: 0.01
• Chart type: Combo - Area and Area

The finer step increment (0.01) returns a left margin of the blue tail area that visually appears to be vertical.

### Peltier :: combo area - XY with smoothed lines :: step [modified date]

Peltier (2013) uses includes an XY type chart with secondary axis and X values treated as dates.

• Worksheet: Peltier #1
• Chart type: Combo - Area and XY

See Peltier (2013) for details.

## 2. Discussion

An examination of figure 1, items 2 and 3 suggests that the area plot with fine increments is equivalent to the Peltier XY plot, at least for a tail area.