Respuesta :
Answer:
The area of the shaded region under the standard normal curve is 0.4834.
Step-by-step explanation:
A random variable X is said to have a normal distribution with mean, µ and variance σ².
Then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z [tex]\sim[/tex] N (0, 1).
The distribution of these z-variates is known as the standard normal distribution.
Compute the area under the curve between -2.13 and 0 as follows:
[tex]P(-2.13<Z<0)=P(Z<0)-P(Z<-2.13)[/tex]
[tex]=0.50-0.01659\\=0.48341\\\approx 0.4834[/tex]
Thus, the area of the shaded region under the standard normal curve is 0.4834.
Using the normal distribution, it is found that the area of the shaded region is of 0.4833.
- In a normal distribution, our test statistic is the z-score, which measures how many standard deviations a measure is from the mean.
- Each z-score has an associated p-value, which is given at the z-table, and represents the percentile of a measure or or the z-score, which is the area to the left under the normal curve.
- The area between two z-scores is the subtraction of their p-values.
In this problem, we want the area between Z = -2.13 and Z = 0.
- Z = 0 has a p-value of 0.5.
- Z = -2.13 has a p-value of 0.0166.
0.5 - 0.0166 = 0.4833
The area of the shaded region is of 0.4833.
A similar problem is given at https://brainly.com/question/22940416
