Question

​Determine the mean, which is the value of λ, for each scenario below:

1. A fifth-grader averages three grammatical errors per paragraph. What is his average for four paragraphs?

2. A surveillance officer reports two incidents of shoplifting per month, on average. How many incidents of shoplifting on average are reported per year?

3. Baggage handlers at a certain airport move an average of 1500 bags on an eight-hour shift. On average, how many bags are moved per hour?

4. An assembly line, on average, produces 1 defective part for every 100 parts that roll off the line. What is the average number of defects for a group of 20 parts?

5. You average 70 heartbeats per minute. What is the average number of heartbeats you have in 10 seconds?

Answer 1

To find the averages in each scenario, you need to multiply, divide, or multiply and divide the given values based on the given information.

Step-by-step explanation:

1. To determine the average for four paragraphs, we need to multiply the average number of grammatical errors per paragraph by the number of paragraphs. In this case, the fifth-grader averages three grammatical errors per paragraph, so for four paragraphs, the average is 3 * 4 = 12 grammatical errors.

2. To determine the incidents of shoplifting per year, we need to multiply the average incidents per month by the number of months in a year. In this case, the surveillance officer reports an average of two incidents of shoplifting per month, so for a year, the average is 2 * 12 = 24 incidents of shoplifting.

3. To determine the bags moved per hour, we need to divide the average number of bags moved in an eight-hour shift by eight. In this case, the baggage handlers move an average of 1500 bags in an eight-hour shift, so per hour, the average is 1500 / 8 = 187.5 bags moved.

4. To determine the average number of defects for a group of 20 parts, we need to multiply the average number of defects for every 100 parts by the number of groups. In this case, the assembly line produces an average of 1 defective part for every 100 parts, so for 20 parts, the average is (1/100) * 20 = 0.2 defects.

5. To determine the average number of heartbeats in 10 seconds, we need to multiply the average number of heartbeats per minute by the number of minutes in 10 seconds (10/60). In this case, you average 70 heartbeats per minute, so in 10 seconds, the average is (70 * 10/60) = 11.67 heartbeats.