The variance of 25 observations is 6. If each observation is multiplied by 3, then the new variance of the resulting observations 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: Identify the given values. \[ \text{Old Variance}=6, \qquad k=3. \]

Step 2: Apply the variance transformation formula. \[ \text{New Variance} = 3^2\times6. \] \[ = 9\times6. \] \[ = 54. \] Conclusion: \[ {54} \]

\(\text{Length (in mm)}\)	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

The variance of 25 observations is 6. If each observation is multiplied by 3, then the new variance of the resulting observations is

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The Correct Option is C

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