Question

A brand of corn flakes come in a box that says it holds 32 ounces of cereal. The manufacturer says that the weights of corn flakes have a normal distribution with a standard deviation of 0.29 ounces. Use the Cumulative Z-Score Table to answer the following questions. The Z-Score Table can be found below by selecting "Read". Round all answers to the nearest box. If the manufacturer ships 860,000 boxes then... ...how many boxes weigh less than 31.768 ounces? boxes ...how many boxes weigh more than 31.768 ounces? boxes ...how many boxes weigh less than 31.565 ounces? boxes ...how many boxes weight more than 31.565 ounces? boxes ...how many boxes weigh between 31.565 and 31.768 ounces? boxes

Answer 1

To determine the number of boxes that weigh less than or more than a given weight, we can calculate the z-score for that weight and use the cumulative Z-Score Table. For the given question, we find that approximately 153,869 boxes weigh less than 31.768 ounces, 750,574 boxes weigh more than 31.565 ounces, and 44,443 boxes weigh between 31.565 and 31.768 ounces.

Step-by-step explanation:

To find the number of boxes that weigh less than 31.768 ounces, we need to calculate the z-score for this weight and use the cumulative Z-Score Table to find the corresponding probability. The z-score is calculated as (31.768 - 32) / 0.29 = -0.928. From the cumulative Z-Score Table, we find that the probability associated with a z-score of -0.928 is approximately 0.1788. Multiplying this probability by the total number of boxes (860,000) gives us 153,868.8 boxes, rounded to the nearest whole number. Therefore, approximately 153,869 boxes weigh less than 31.768 ounces.

To find the number of boxes that weigh more than 31.768 ounces, we subtract the number of boxes that weigh less than 31.768 ounces from the total number of boxes. Therefore, approximately 706,131 boxes weigh more than 31.768 ounces.

To find the number of boxes that weigh less than 31.565 ounces, we repeat the steps above with the weight of 31.565 ounces. The z-score is calculated as (31.565 - 32) / 0.29 = -1.138. From the cumulative Z-Score Table, we find that the probability associated with a z-score of -1.138 is approximately 0.1271. Multiplying this probability by the total number of boxes (860,000) gives us 109,426 boxes, rounded to the nearest whole number. Therefore, approximately 109,426 boxes weigh less than 31.565 ounces.

To find the number of boxes that weigh more than 31.565 ounces, we subtract the number of boxes that weigh less than 31.565 ounces from the total number of boxes. Therefore, approximately 750,574 boxes weigh more than 31.565 ounces.

To find the number of boxes that weigh between 31.565 and 31.768 ounces, we subtract the number of boxes that weigh less than 31.565 ounces (109,426) from the number of boxes that weigh less than 31.768 ounces (153,869). Therefore, approximately 44,443 boxes weigh between 31.565 and 31.768 ounces.