Questions: The following data represent the weights (in grams) of a random sample of 50 candies. 0.96, 0.89, 0.82, 0.82, 0.84, 0.89, 0.98, 0.86, 0.85, 0.86, 0.81, 0.87, 0.77, 0.87, 0.86, 0.82, 0.73, 0.84, 0.74, 0.84, 0.94, 0.77, 0.79, 0.92, 0.82, 0.93, 0.87, 0.91, 0.81, 0.75, 0.96, 0.82, 0.77, 0.74, 0.84, 0.77, 0.83, 0.86, 0.89, 0.79, 0.72, 0.86, 0.71, 0.73, 0.83, 0.82, 0.87, 0.93, 0.92, 0.83 (a) Determine the sample standard deviation weight. n 22 s= gram (Round to two decimal places as needed.)

Solution Steps

To find the mean \( \mu \) of the weights of the candies, we use the formula:

\[ \mu = \frac{\sum x_i}{n} \]

where \( n \) is the number of candies (50) and \( \sum x_i \) is the sum of all weights. The sum of the weights is approximately \( 41.92 \).

Thus, we have:

\[ \mu = \frac{41.92}{50} = 0.84 \]

The variance \( \sigma^2 \) is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} \]

Substituting the values, we find that the variance is \( 0.0 \).

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{0.0} = 0.07 \]

Final Answer