If the first quartile is 142 and the semi-interquartile range is 18, then the third quartile is:

Question

If two numbers \( p \) and \( q \) are chosen randomly from the set \( \{1, 2, 3, 4\} \) with replacement, what is the probability that \( p^2 \geq 4q \)?

Answer 1

Step 1: Use the given information. Given, \[ Q_1=142 \] and \[ \frac{Q_3-Q_1}{2}=18. \] Therefore, \[ \frac{Q_3-142}{2}=18. \]

Step 2: Solve for \(Q_3\). Multiplying by \(2\), \[ Q_3-142=36. \] Adding \(142\) to both sides, \[ Q_3=178. \] Conclusion: \[ {178} \] Hence, the correct answer is Option (C).

\(\text{Length (in mm)}\)	70-80	80-90	90-100	100-110	110-120	120-130	130-140
\(\text{Number of leaves}\)	3	5	9	12	5	4	2

Economic System	Characteristics
a. Capitalism	i. Private ownership of resources; market-driven economy with minimal government intervention
b. Socialism	ii. Government ownership of key industries; centralized economic planning
c. Mixed Economy	iii. Combination of private and government ownership; focus on social welfare and regulation
d. Market Economy	iv. Private ownership with some government regulation; competition and market forces determine economic outcomes

If the first quartile is 142 and the semi-interquartile range is 18, then the third quartile is:

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The Correct Option is C

Solution and Explanation

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