Determine P(-k≤X≤k) when X follows the standard normal distribution - High school Statistics & Probabilities Exercises

X follows \mathcal{N}\left(0{,}1\right).

Determine P\left(-1.4 \lt X \lt 1.4\right) using the following table.

P\left(-1.4 \lt X \lt 1.4\right)=0.7\ 576

P\left(-1.4 \lt X \lt 1.4\right)=0.808

P\left(-1.4 \lt X \lt 1.4\right)=0.9\ 192

P\left(-1.4 \lt X \lt 1.4\right)=0.8\ 384

X follows \mathcal{N}\left(0{,}1\right).

Determine P\left(-2.3 \lt X \lt 2.3\right) using the following table.

Insert a table of a normal distribution.

P\left(-2.3 \lt X \lt 2.3\right)=0.9\ 786

P\left(-2.3 \lt X \lt 2.3\right)=0.9\ 182

P\left(-2.3 \lt X \lt 2.3\right)=0.9\ 218

P\left(-2.3 \lt X \lt 2.3\right)=0.9\ 281

X follows \mathcal{N}\left(0{,}1\right).

Determine P\left(-1.76 \lt X \lt 1.76\right) using the following table.

P\left(-1.76 \lt X \lt 1.76\right)=0.9\ 612

P\left(-1.76 \lt X \lt 1.76\right)=0.9\ 216

P\left(-1.76 \lt X \lt 1.76\right)=0.9\ 621

P\left(-1.76 \lt X \lt 1.76\right)=0.8\ 575

X follows \mathcal{N}\left(0{,}1\right).

Determine P\left(-0.5 \lt X \lt 0.5\right) using the following table.

P\left(-0.5 \lt X \lt 0.5\right)=0.398

P\left(-0.5 \lt X \lt 0.5\right)=0.1\ 417

P\left(-0.5 \lt X \lt 0.5\right)=0.2\ 174

P\left(-0.5 \lt X \lt 0.5\right)=0.4\ 129

X follows \mathcal{N}\left(0{,}1\right).

Determine P\left(-2 \lt X \lt 2\right) using the following table.

P\left(-2 \lt X \lt 2\right)=0.9\ 544

P\left(-2 \lt X \lt 2\right)=0.8\ 572

P\left(-2 \lt X \lt 2\right)=0.8\ 147

P\left(-2 \lt X \lt 2\right)=0.2

X follows \mathcal{N}\left(0{,}1\right).

Determine P\left(-1.37 \lt X \lt 1.37\right) using the following table.

P\left(-1.37 \lt X \lt 1.37\right)=0.8\ 294

P\left(-1.37 \lt X \lt 1.37\right)=0.7\ 185

P\left(-1.37 \lt X \lt 1.37\right)=0.6\ 076

P\left(-1.37 \lt X \lt 1.37\right)=0.7\ 305