Answer:
0.815
Step-by-step explanation:
First, find the z-scores.
z = (x − μ) / σ
z₁ = (8 − 10) / 1
z₁ = -2
z₂ = (11 − 10) / 1
z₂ = 1
P(-2 < Z < 1) = P(Z < 1) − P(Z < -2)
Use a chart, calculator, or the empirical rule to find the probability.
Using the empirical rule:
P(-2 < Z < 1) = 0.84 − 0.025
P(-2 < Z < 1) = 0.815
Using a chart:
P(-2 < Z < 1) = 0.8413 − 0.0228
P(-2 < Z < 1) = 0.8185
The probability of selecting number will be "0.8185".
According to the question,
Z-score be:
→ [tex]z = \frac{x - \mu}{\sigma}[/tex]
By substituting the values,
[tex]z_1= \frac{8-10}{1}[/tex]
[tex]= -2[/tex]
[tex]z_2 = \frac{11-10}{1}[/tex]
[tex]= 1[/tex]
By using the empirical rule,
→ [tex]P(-2 < Z<1) = P(Z<1)-P(Z<-2)[/tex]
[tex]= 0.84-0.025[/tex]
[tex]= 0.815[/tex]
By using chart,
→ [tex]P(-2 < Z < 1) = 0.8413-0.0228[/tex]
[tex]= 0.8185[/tex]
Thus the above response is correct.
Find out more information about probability here:
https://brainly.com/question/25870256
