**Probability of Aircraft Overloading** In ensuring flight safety, a pilot must confirm that the total weight does not exceed the aircraft's maximum allowable load. An aircraft with a capacity of 39 passengers, including fuel and baggage, allows for a total passenger load of 6,396 lbs. If the plane is at full capacity with male passengers, overloading occurs when the mean weight per passenger exceeds \( \frac{6,396}{39} = 164 \) lbs.**Question:**What is the probability that the aircraft is overloaded? Should the pilot take corrective action? Assume the weights of men are normally distributed with a mean of 182.4 lbs and a standard deviation of 39.7 lbs.**Solution Approach:**1. Standardize the problem using the normal distribution model.2. Calculate the probability that the average weight is greater than 164 lbs.3. Determine if any corrective actions are necessary based on the probability calculated.**Calculation:**- Mean (\(\mu\)) = 182.4 lbs- Standard deviation (\(\sigma\)) = 39.7 lbs- Desired average weight threshold = 164 lbsThe probability is approximately \[ \_\_\_\_ \].(Round to four decimal places as needed.)**Action:**Assess whether this probability warrants action to prevent overloading.*Note: Detailed calculations involving Z-scores and normal distribution tables might be required to find the exact probability value.*

Answered: Image /qna-images/answer/32b220da-4b0f-4c8b-be54-448a2293c3f6.jpg

Answered: Before every flight, the pilot must…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The Bombardier Dash 8 aircraft can carry 38 passengers, and a flight has fuel that allows for a total passenger load of 6200 lbs. The pilot sees that the plane is full and all passengers are men.1. What would the average weight of the 38 passengers have to be in order to exceed 6200 lbs?2. What is the probability that the plane is overloaded? Assume the weights of men are normally distributed with a mean of 189 lbs and a standard deviation of 39 lbs.
A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Data from a portion of this study are contained in the Excel Online file below. Risk is interpreted as the probability (times 100) that a person will have a stroke over the next 10-year period. For the smoker variable, 1 indicates a smoker and 0 indicates a nonsmoker. Construct a spreadsheet to answer the following questions.
A drug test correctly gives a positive result 90 percent of the time. However, 3 percent of the time, it incorrectly gives a positive result. This is known as a false positive. Suppose that 7 percent of the people to be tested will have one or more of the drugs being tested for in their system. What is the probability that a randomly chosen person will have get a positive test result? Your answer should be to 4 decimal places.
A drug test correctly gives a positive result 88 percent of the time. However, 3 percent of the time, it incorrectly gives a positive result. This is known as a false positive. Suppose that 5 percent of the people to be tested will have one or more of the drugs being tested for in their system. What is the probability that a randomly chosen person will have get a positive test result? Your answer should be to 4 decimal places.
One half of the people in the United States own individual stocks. In a random sample of 12 people, what is the probability that the number owning individual stocks is less than 4. Round to 3 decimal places.
A real estate agent has 18 properties that she shows. She feels that there is a 50% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling less than 5 properties in one week. Round your answer to four decimal places.
On average there are 3 leaks for every 100 miles of a pipeline. What is the probability that a 50-mile section of the pipeline has at least 1 leak?
If a seed is planted, it has a 61% chance of growing into a healthy plant. Let X be the number of seeds grow into healthy plants when 57 seeds are planted. What is the distribution of X? Please show the following answers to 4 decimal places. What is the probability that exactly 24 seeds grow into healthy plants? What is the probability that at most 24 seeds grow into healthy plants?
According to TMUSS Quarterly (Totally Made-Up Sports Statistics) April 2017, the probability that the Tampa Bay Buccaneers defense will have 3 or more sacks in the game is 0.07. The probability that the Bucs will both score a touchdown on their opening drive and have 3 or more sacks in the game is 0.34. The is the probability that they will either score a touchdown on the opening drive or have 3 or more sacks in the game is 0.20. What is the probability that the Bucs will score a touchdown on their first drive? Answer in decimal form. Round to two decimal places as needed.
A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and O indicating a nonsmoker. Systolic Blood Risk Age Smoker Pressure 10 56 145 No 25 55 160 No 10 60 156 No 58 88 175 Yes 27 60 195 Yes 49 75 185 Yes 15 55 156 Yes 32 77 120 No 35 80 135 No 15 78 98 No 22 71 152 No 36 70 173 Yes 15 67 135 No 48 77 209 No 14 60 199 No 36 82 119 Yes 8 65 166 No 34 82 125 No 3 61 117 No 39 60 208 Yes (a) Develop an estimated multiple regression equation that relates risk of a stroke to the person's age, systolic blood pressure, and whether the person is a smoker. Let x1 represent the person's age. Let x2 represent…
A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker. Risk Age SystolicBloodPressure Smoker 11 58 152 Yes 24 65 163 No 13 58 155 No 56 86 177 Yes 27 59 196 Yes 51 76 189 Yes 18 56 155 Yes 31 78 120 No 37 80 135 Yes 15 78 98 No 22 71 152 No 36 70 173 Yes 15 67 135 Yes 48 77 209 Yes 15 60 199 No 36 82 119 Yes 8 66 166 No 34 80 125 Yes 3 62 117 No 38 59 209 Yes (a) Develop an estimated multiple regression equation that relates risk of a stroke to the person's age, systolic blood pressure, and whether the person is a…
According to TMUSS Quarterly (Totally Made-Up Sports Statistics) April 2017, the probability that the Tampa Bay Buccaneers defense will have 3 or more sacks in the game is 0.05. The probability that the Bucs will both score a touchdown on their opening drive and have 3 or more sacks in the game is 0.25. The is the probability that they will either score a touchdown on the opening drive or have 3 or more sacks in the game is 0.25. What is the probability that the Bucs will score a touchdown on their first drive? Answer in decimal form. Round to two decimal places as needed. Your Answer:

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