Question: 1 Fill in the Blank 5 points The average time for a student to complete this quiz is 24 minutes…

1 Fill in the Blank 5 points The average time for a student to complete this quiz is 24 minutes with a standard deviation of 2 minutes. What is the range of minutes needed for the middle 68% of quiz times? Complete the sentence below. The middle 68% of all people finish the quiz somewhere between 22 and 26 minutes. 2 Formula 5 points How many meters per second are in 44 miles per hour? Round to one decimal. 19.7 3 Formula 8 points During a heavy storm, rain falls for 3.8 hours through the night. A weather station monitors the rain by measuring the milliliters of water it takes to fill a container. How many milliliters of rain will fill the container if the rain falls at a rate of 3 quarts per 41 minutes? Round to one decimal. 15,787.9 4 Numeric 5 points The average amount of time to finish this quiz is 26 minutes with a standard deviation of 1.2 minutes. What is the probability that you will finish this quiz in 25.1 minutes or less? Write your answer as a percentage with 2 decimals. 22.64 5 Formula 4 points Convert 1.395 dekagrams into decigrams. Round to one decimal. 139.5

Solution

1. The average time for a student to complete the quiz is 24 minutes with a standard deviation of 2 minutes. The middle 68% of quiz times fall within one standard deviation of the mean. Therefore, the range of minutes is: Mean = 24 minutes Standard deviation = 2 minutes The middle 68% lie between: \[ 24 - 2 = 22 \text{ minutes} \] \[ 24 + 2 = 26 \text{ minutes} \] 2. To convert 44 miles per hour to meters per second, use the conversion factors \(1 \text{ mile} = 1609.34 \text{ meters}\) and \(1 \text{ hour} = 3600 \text{ seconds}\): \[ 44 \text{ miles/hour} \times \frac{1609.34 \text{ meters}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3600 \text{ seconds}} \] \[ = \frac{44 \times 1609.34}{3600} \approx 19.7 \text{ meters/second} \] 3. To calculate how many milliliters of rain will fill the container, first convert the quarts to milliliters using \(1 \text{ quart} = 946.353 \text{ milliliters}\). Rate of rain = \(3\) quarts per \(41\) minutes \[ \frac{3 \text{ quarts}}{41 \text{ minutes}} \times \frac{946.353 \text{ milliliters}}{1 \text{ quart}} \times 3.8 \text{ hours} \times 60 \text{ minutes/hour} \] \[ = \frac{3 \times 946.353}{41} \times 3.8 \times 60 \approx 15787.9 \text{ milliliters} \] 4. For the probability of finishing the quiz in 25.1 minutes or less, use the Z-score formula: Mean = 26 minutes Standard deviation = 1.2 minutes \[ Z = \frac{25.1 - 26}{1.2} = -0.75 \] Using a standard normal distribution table, the probability corresponding to \(Z = -0.75\) is approximately 22.66%. 5. To convert 1.395 dekagrams to decigrams: \[ 1 \text{ dekagram} = 10 \text{ grams} \] \[ 1 \text{ gram} = 10 \text{ decigrams} \] \[ 1.395 \text{ dekagrams} \times 10 \times 10 = 139.5 \text{ decigrams} \]