Answer:
Option B is correct.
Confidence interval = 3 plus or minus 2.36 times square root of 2.4 squared over 120 plus 1.8 squared over 120
Explanation:
Hamburger hop = N₁ (32, 2.4²)
Cheesy chops = N₂ (29, 1.8²)
The combined distribution is the difference between the means of Hamburger hop and Cheesy Chops
N = (N₁ - N₂)
For two distributions (N₁ and N₂) with means p and q and variance x and y,
The new mean of a combined distribution (aN₁ + bN₂) is (ap + bq)
And the new variance = a²x + b²y
So, for our distribution,
N₁ (32, 2.4²)
N₂ (29, 1.8²)
The new mean of N = (N₁ - N₂) will be (32 - 29) = 3
The new variance of N = (N₁ - N₂) will be
(1²)(2.4²) + (-1)²(1.8²) = 2.4² + 1.8²
And the standard deviation = √[2.4² + 1.8²]
And the confidence interval is given as
Confidence interval = (Sample mean) ± (Margin of error)
Sample mean = 3
Margin of error = (critical value) × (standard deviation of the distribution of sample means)
Critical value for a 98% confidence interval is 2.36
(standard deviation of the distribution of sample means) = (standard deviation/√n)
n = sample size = 120
standard deviation = √[2.4² + 1.8²]
(standard deviation of the distribution of sample means) = {√[2.4² + 1.8²]/√120}
= √[(2.4² + 1.8²)/120]
Margin of error = 2.36 × √[(2.4² + 1.8²)/120]
Confidence interval = (Sample mean) ± (Margin of error)
Confidence interval = 3 ± {2.36 × √[(2.4² + 1.8²)/120]}
Confidence interval = 3 plus or minus 2.36 times square root of 2.4 squared over 120 plus 1.8 squared over 120
Hope this Helps!!!