Solve a problem

Normal distribution and z-scoresStatistics and probabilityHigh schoolabout 0:33

Find P(-2 < Z < 2) for a standard normal variable: animated lesson

A narrated, step-by-step normal distribution and z-scores video lesson with captions. Final answer: P(-2 < Z < 2) ≈ 0.9545 (95.45%).

SpeedLanguage

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.2 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
Find P(-2 < Z < 2) for a standard normal variable.
2. Step by step
1. $\Phi(2) \approx 0.97724987,\quad \Phi(-2) \approx 0.022750132$
  Find the left areas of both z-scores
2. $P(-2 < Z < 2) \approx 0.95449974$
  Subtract
3. The answer
$P(-2 < Z < 2) \approx 0.9545$
P(-2 < Z < 2) ≈ 0.9545 (95.45%)

Transcript

The problem. Here is the problem: Find P(negative 2 less than Z less than 2) for a standard normal variable. P(z₁ less than Z less than z₂): area between.

Step by step. Find the left areas of both z-scores. Subtract.

The answer. So the answer is P(negative 2 less than Z less than 2) approximately 0.9545 (95.45 percent). 95.45 percent of a normal distribution lies between these two z-scores.

About normal distribution and z-scores

Standardise values with z-scores and find normal probabilities.

Find P(-2 < Z < 2) for a standard normal variable (Lesson)