If the range of a set of observations on a variable X is known to be 25 and if Y= 40+3X, then what is the range of the set of corresponding observations on y?

Options

A. 25
B. 40
C. 75
D. 115

Answer

To solve the problem step by step, we will follow the mathematical concepts related to the range of a set of observations.

### Step 1: Understand the given information
We are given:
- The range of observations on variable \( X \) is \( 25 \).
- The relationship between \( Y \) and \( X \) is given by the equation \( Y = 40 + 3X \).

### Step 2: Identify the formula for the range of \( Y \)
The formula for the range of \( Y \) when \( Y \) is expressed in the form \( Y = a + bX \) is:
\[ \text{Range of } Y = |b| \times \text{Range of } X \]
where:
- \( b \) is the coefficient of \( X \) (in this case, \( b = 3 \)).
- The range of \( X \) is given as \( 25 \).

### Step 3: Calculate the range of \( Y \)
Using the formula:
\[ \text{Range of } Y = |3| \times 25 \]
Calculating this gives:
\[ \text{Range of } Y = 3 \times 25 = 75 \]

### Step 4: Conclusion
Thus, the range of the set of corresponding observations on \( Y \) is \( 75 \).

### Final Answer:
The range of the set of corresponding observations on \( Y \) is \( 75 \).

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