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Answer :
The combined mean weight of freshman boys and girls at Midtown University is 285 lbs, and the standard deviation is approximately 10.82 lbs.
Calculating the Mean and Standard Deviation of Combined Weights at Midtown University
To find the mean and standard deviation of a new distribution formed by adding the weights of freshman boys and girls, we start with the given statistics:
- Boys: Mean = 170 lbs, Standard Deviation = 9 lbs
- Girls: Mean = 115 lbs, Standard Deviation = 6 lbs
Mean of the New Distribution
The mean of the combined distribution is the sum of the individual means:
Mean = 170 lbs + 115 lbs = 285 lbs
Standard Deviation of the New Distribution
Since the weights are independent, the variance of the combined distribution is the sum of the individual variances. Variance is the square of the standard deviation:
- Variance (boys) = 92 = 81
- Variance (girls) = 62 = 36
Combined Variance = 81 + 36 = 117
The standard deviation of the new distribution is the square root of the combined variance:
Standard Deviation = √117 ≈ 10.82 lbs
Thus, the new distribution has a mean of 285 lbs and a standard deviation of 10.82 lbs.
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