Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
The probability that x will be less than 55 is 0.1587.
Given,
In the Question;
X is a normally distributed random variable .
Mean µ = 50
Standard deviation (σ) = 5
X = 55
To solve the probability that x will be less than 55.
Now, According to the question:
The standardize the Random Variable X with the Standardized Normal Distribution Z Variable using the relationship:
Z = (X - µ) ÷ σ
Normal Distribution Tables of the function:
Φ(z) = P(Z ≤ z)
P(X > 55) = P(Z > ((55 - 50) ÷ 5))
P(X > 55) = P(Z > 5 ÷ 5)
P(X > 55) = P(Z > 1)
So,
P(X > 55) = P(Z > 1)
P(X > 55) = 1 - P(Z < 1)
Using the Standard Normal Table,
P(X > 55) = 1 - Φ(1)
P(X > 55) = 1 - 0.8413
P(X > 55) = 0.1587
Hence, The probability that x will be less than 55 is 0.1587.
Learn more about the Normal distribution at:
https://brainly.com/question/13759327
#SPJ4
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
