(a) The area of the shaded region is 0.2709.
(b) The area of the shaded region is 0.3520.
(c) The area of the shaded region is 0.5555.
(d) The area of the shaded region is 0.6197
What is standard normal curve?
The horizontal axis is approached but never touched by the standard normal curve as it extends indefinitely in both directions. The center of the bell-shaped standard normal curve, which has a z=0 slope, is. Nearly all of the standard normal curve's area lies between z = 3 and z = 3.
The shaded area under the standard normal curve are,
1) Find, P[Z > 0.61 ]
= P[Z > 0.50]
= 1 - P[Z < -0.50]
= 1 - 0.7291 ( use z table)
= 0.2709
The area of the shaded region is 0.2709.
2) Find, P[Z < -0.38 ]
= P[Z < -0.38 ]
= 0.3520 ... ( use z table)
The area of the shaded region is 0.3520.
3) Find, P( -0.58 < Z < 0.98 )
= P(Z < 0.98 ) - P(Z < -0.58 )
= 0.8365 - 0.2810 ......(using z-table)
= 0.5555
The area of the shaded region is 0.5555.
4) Find , P( -0.11 < Z > 0.98 )
= 1 - P(Z < 0.98 ) - P(Z < -0.11 )
= 1 - ( 0.8365 - 0.4562 ) ......(using z-table)
= 1 - 0.3803
= 0.6197
Hence, the area of the shaded region is 0.6197.
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