### Educational Exercise: Probability and Normal Distribution in Animal PregnanciesThe exercise explores the normal distribution characteristics of a particular animal's pregnancy lengths, which are approximately normally distributed with a mean ($\mu$) of 271 days and a standard deviation ($\sigma$) of 16 days. The tasks are as follows:#### Questions:1. **Proportion of Long Pregnancies:** - **Question:** What proportion of pregnancies lasts more than 299 days? - **Task:** Calculate using the normal distribution. - **Priority:** Round your answer to four decimal places.2. **Proportion of Mid-Range Pregnancies:** - **Question:** What proportion of pregnancies lasts between 251 and 279 days? - **Task:** Use the normal distribution rules to find the probability of occurrences within this range. - **Priority:** Round your answer to four decimal places.3. **Probability of Short Pregnancies:** - **Question:** What is the probability that a randomly selected pregnancy lasts no more than 263 days? - **Task:** Determine the cumulative probability for this event. - **Priority:** Round your answer to four decimal places.4. **Probability of Very Preterm Births:** - **Question:** A "very preterm" baby is one whose gestation period is less than 235 days. Are very preterm babies unusual? - **Task:** Calculate the probability and assess whether this event is unusual by comparing the probability to 0.05. - **Priority:** Round your answer to four decimal places and decide on the unusualness of the event.#### Additional Guidance:- For each calculation, refer to the properties of the normal distribution curve and use statistical tables or software as necessary.- Understand that probabilities less than 0.05 are typically considered unusual in statistical contexts.- This exercise helps in applying statistical methods to real-world biological data, enhancing understanding of variability in natural processes.

Answered: Image /qna-images/answer/b672a2f4-410b-48fa-a1a8-8bdc11b93564.jpg

Answered: K The lengths of a particular animal's…

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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Based on historical data, your manager believes that 25% of the company's orders come from first- time customers. A random sample of 83 orders will be used to estimate the proportion of first-time- customers. What is the probability that the sample proportion is between 0.21 and 0.35? Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations. Answer = (Enter your answer as a number accurate to 4 decimal places.)
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28% below the target pressure. Suppose the target tire pressure of a certain car is 28 psi (pounds per square inch.) (a) At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) When the tire pressure is (Click to select) psi. (b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 3 psi. If the car's average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.) Probability (c) The manufacturer's recommended correct inflation range is 26 psi to 30 psi. Assume the tires' average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire's inflation is within the recommended range? (Round your intermediate calculations and final answer to 4 decimal places.) Probability 18 of 19 Next > Prev…
Based on historical data, your manager believes that 40% of the company's orders come from first- time customers. A random sample of 223 orders will be used to estimate the proportion of first- time-customers. What is the probability that the sample proportion is between 0.24 and 0.43? Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations. Answer = (Enter your answer as a number accurate to 4 decimal places.) Question Help: Message instructor Submit Question 80 888 F2 F3 F4 F5 F6 F7 F8 @ $ & 2 8. < CO # 3
Jim is a 60-year-old male in reasonably good health. He wants to take out a $50,000 term (that is, straight death benefit) life insurance policy until he is 65. The policy will expire on his 65th birthday. The probability of death in a given year is provided by the Vital Statistics Section of the Statistical Abstract of the United States (116th edition) X=age 60 61 62 63 64 P(death at this age) 0.01191 0.01292 0.01396 0.01503 0.011613 Jim is applying to Big Rock Insurance Company for his term insurance policy. What is the probability that Jim will die in his 60th year? Using this probability and the $50,000 death benefit, what is the expected cost to Big Rock Insurance? Repeat part (a) for years 61, 62, 63, and 64. What would be the total expected cost to Big Rock Insurance over the years 60 through 64? If Big Rock Insurance wants to make a profit of $700 above the expected total cost paid out for Jim’s death, how much should it charge for the policy?…
The amount X spent (in $) by customers in the grocery store express lane follows some right-skewed distribution with mean $24 and standard deviation $15. 18. What is the approximate probability that the next 40 customers spend less than $1,000 in total? (A) 0.5199 (B) 0.6064 (C) 0.6628 (D) 0.5784 (E) 0.6331
Based on historical data, your manager believes that 41% of the company's orders come from first- time customers. A random sample of 84 orders will be used to estimate the proportion of first-time- customers. What is the probability that the sample proportion is between 0.33 and 0.48? Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations. Answer = (Enter your answer as a number accurate to 4 decimal places.) Question Help: Message instructor Submit Question DI 80 88 F9 F6 F7 F8 F3 F4 F5 @ # $ & 3 4 6. 7 8. W R Y S D G H J V
2. A study propose the Weibull distribution (a = 2.0, B= 200) as a model for time to failure of solid insulating specimens subject to AC voltage. a) What is the probability that a specimen's lifetime is at least 250? Round your answer to four decimal places. b) What is the median time to failure? Round you answer to two decimal places.
Based on historical data, your manager believes that 43% of the company's orders come from first- time customers. A random sample of 90 orders will be used to estimate the proportion of first-time- customers. What is the probability that the sample proportion is between 0.3 and 0.44? Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations. Answer = (Enter your answer as a number accurate to 4 decimal places.) Question Help: Message instructor Submit Question Previous 80 888 F3 F4 F5 F6 F7 F8 F9 $ & 2 4 6. 7 8. W E Y U J K この # 3
Based on historical data, your manager believes that 33% of the company's orders come from first-time customers. A random sample of 207 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.32 and 0.5? Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations. Answer = (Enter your answer as a number accurate to 4 decimal places.)

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