Answer:
0.8572 is the required probability.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 50
Standard Deviation, σ = 7
We are given that the distribution of random variable X is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(x between 35 and 58)
[tex]P(35 < x < 58)\\\\ = P(\displaystyle\frac{35 - 50}{7} \leq z \leq \displaystyle\frac{58-50}{7}) = P(-2.142 \leq z \leq 1.142)\\\\= P(z \leq 1.142) - P(z < -2.142)\\= 0.8733- 0.0161 = 0.8572= 85.72\%[/tex]
0.8572 is the required probability.
Answer:
The probability is 85.7%
Step-by-step explanation:
Given information:
Bounds condition=([tex]P(35\leq x \leq58)[/tex]
Mean value
[tex]\mu=50[/tex]
Standard deviation
[tex]\sigma=7[/tex]
Curve is normally distributed so,
We can use
[tex]z_{score}=\frac{X-\mu}{\sigma}[/tex]
For X=35
[tex]z_{score}=\frac{X-\mu}{\sigma}=\frac{35-50}{7}=-2.142[/tex]
For X=50
[tex]z_{score}=\frac{X-\mu}{\sigma}=\frac{58-50}{7}=1.142[/tex]
[tex]P(z\leq1.142)-P(z\leq-2.142)\\0.873-1.016=0.857[/tex]
The probability is 85.7%.
For more details please refer link:
https://brainly.com/question/5286270?referrer=searchResults
