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If 𝑋 follows normal distribution with 𝜇 = 50 and 𝜎 = 10, what is the value of 𝑃(𝑥 ≤
60/𝑥 > 50) ?
Note: [𝜙(1) = 0.8613]∗?
60/𝑥 > 50) ?
Note: [𝜙(1) = 0.8613]∗?
Most Upvoted Answer
If 𝑋 follows normal distribution with 𝜇 = 50 and 𝜎 = 10, what is th...
Understanding the Problem
To calculate \( P(X \leq 60 | X > 50) \), we first need to find \( P(X \leq 60) \) and \( P(X > 50) \).
Step 1: Finding \( P(X \leq 60) \)
- Given \( \mu = 50 \) and \( \sigma = 10 \), we standardize the value 60.
- Calculate the z-score:
\[
z = \frac{X - \mu}{\sigma} = \frac{60 - 50}{10} = 1
\]
- Using the given \( \phi(1) = 0.8613 \):
\[
P(X \leq 60) = 0.8613
\]
Step 2: Finding \( P(X > 50) \)
- Standardize the value 50:
\[
z = \frac{50 - 50}{10} = 0
\]
- Since \( P(X \leq 50) = \phi(0) = 0.5 \):
\[
P(X > 50) = 1 - P(X \leq 50) = 1 - 0.5 = 0.5
\]
Step 3: Applying Conditional Probability
- To find \( P(X \leq 60 | X > 50) \), use the formula:
\[
P(X \leq 60 | X > 50) = \frac{P(X \leq 60 \cap X > 50)}{P(X > 50)}
\]
- Since \( P(X \leq 60 \cap X > 50) = P(X \leq 60) - P(X \leq 50) \):
\[
P(X \leq 50) = 0.5 \quad \Rightarrow \quad P(X \leq 60 \cap X > 50) = 0.8613 - 0.5 = 0.3613
\]
Final Calculation
- Substitute values:
\[
P(X \leq 60 | X > 50) = \frac{0.3613}{0.5} = 0.7226
\]
Conclusion
Thus, the value of \( P(X \leq 60 | X > 50) \) is approximately **0.7226**.
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If 𝑋 follows normal distribution with 𝜇 = 50 and 𝜎 = 10, what is the value of 𝑃(𝑥 ≤ 60/𝑥 > 50) ? Note: [𝜙(1) = 0.8613]∗?
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If 𝑋 follows normal distribution with 𝜇 = 50 and 𝜎 = 10, what is the value of 𝑃(𝑥 ≤ 60/𝑥 > 50) ? Note: [𝜙(1) = 0.8613]∗? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 𝑋 follows normal distribution with 𝜇 = 50 and 𝜎 = 10, what is the value of 𝑃(𝑥 ≤ 60/𝑥 > 50) ? Note: [𝜙(1) = 0.8613]∗? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 𝑋 follows normal distribution with 𝜇 = 50 and 𝜎 = 10, what is the value of 𝑃(𝑥 ≤ 60/𝑥 > 50) ? Note: [𝜙(1) = 0.8613]∗?.
If 𝑋 follows normal distribution with 𝜇 = 50 and 𝜎 = 10, what is the value of 𝑃(𝑥 ≤ 60/𝑥 > 50) ? Note: [𝜙(1) = 0.8613]∗? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 𝑋 follows normal distribution with 𝜇 = 50 and 𝜎 = 10, what is the value of 𝑃(𝑥 ≤ 60/𝑥 > 50) ? Note: [𝜙(1) = 0.8613]∗? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 𝑋 follows normal distribution with 𝜇 = 50 and 𝜎 = 10, what is the value of 𝑃(𝑥 ≤ 60/𝑥 > 50) ? Note: [𝜙(1) = 0.8613]∗?.
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