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Question 7

Mathematics Statistics Easy

Let x<sub>i</sub>, i = 1, 2, ..., n be n observations and w<sub>i</sub> = px<sub>i</sub> + k, i = 1, 2, ..., n where p and k are constants. If the mean of x<sub>i</sub>&#39;s is 48 and standard deviation is 12, whereas the mean of w<sub>i</sub>&#39;s is 55 and standard deviation is 15, then the value of p and k should be

(A) p = 1.25, k = -5
(B) p = -1.25, k = 5
(C) p = 2.5, k = -5
(D) p = 25, k = 5
✓ Correct Answer: Option A Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

For \(w = px + k\): mean(w) = p·mean(x) + k and SD(w) = |p|·SD(x).

\(15 = |p| \times 12 \Rightarrow |p| = 1.25\)

\(55 = 48p + k\). With \(p = 1.25\): \(k = 55 - 60 = -5\).

(\(p = -1.25\) would give \(k = 115\), which is not an option.)

Answer: (A) p = 1.25, k = −5

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