Kyle stocks the shelves at a grocery store. He is responsible for stocking 200 boxes. He wants to know how much weight he lifts throughout the day as he is working. He randomly selects 20 of the boxes and weighs them before stocking them.

Question

Weight of Boxes (pounds)

37

39

47

39

50

42

40

54

50

46

38

46

52

54

42

48

53

49

43

51



Estimate the population total, or the total amount of weight that Kyle lifts throughout the day.

pounds

Answer 1

To estimate the total weight that Kyle lifts throughout the day, we can follow these steps:

1. Calculate the Mean Weight of the Sample: Add up the weights of the 20 boxes and divide by the number of boxes in the sample to get the average weight.

2. Estimate the Total Weight for All Boxes: Multiply the mean weight by the total number of boxes Kyle stocks (200).

Step 1: Calculate the Mean Weight

Let's first sum up the weights:

\[ 37 + 39 + 47 + 39 + 50 + 42 + 40 + 54 + 50 + 46 + 38 + 46 + 52 + 54 + 42 + 48 + 53 + 49 + 43 + 51 = 910 \]

Now, divide the total weight by the number of boxes (20) to find the mean:

\[ \text{Mean weight} = \frac{910}{20} = 45.5 \text{ pounds} \]

Step 2: Estimate the Total Weight

Now, multiply the mean weight by the total number of boxes (200):

\[ \text{Estimated total weight lifted} = 45.5 \times 200 = 9100 \text{ pounds} \]

Thus, the estimated total amount of weight that Kyle lifts throughout the day is 9100 pounds.