Final answer:
The standard deviation of the total weight of a random sample of 6 watermelons and the crate is calculated by squaring the standard deviation of one watermelon, multiplying by the number of watermelons, and summing with the crate's variance. Then, take the square root of this sum to find the total standard deviation.
Step-by-step explanation:
Assuming the weights of small watermelons are independent, the standard deviation of the total weight of a random sample of 6 small watermelons and the crate can be found using the concept of variance of independent random variables. To calculate this standard deviation, you need to square the standard deviation of one watermelon (which should be given in the problem statement but is not provided here), then multiply that squared value by the number of watermelons (in this case, 6). Lastly, add the variance of the crate's weight (which should also be provided). The sum of these variances will give you the total variance of the sample. To find the standard deviation, take the square root of this total variance.
As an example, if the standard deviation of one watermelon's weight is 1.5 lbs, and the variance of the crate is assumed to be negligible or zero, the calculation would be ∑(σ²)= 6*(1.5²), which equals 13.5. The standard deviation of the total weight would then be the square root of 13.5, which is approximately 3.6742 lbs.