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ACT Exam  >  ACT Questions  >  Comprehension:Direction: Based on the followi... Start Learning for Free
Comprehension:
Direction: Based on the following information, answer the questions.
For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:
Find the corresponding probability given a sample of 36
  • a)
    0.8723
  • b)
    0.8
  • c)
    0.745
  • d)
    0.8892
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Comprehension:Direction: Based on the following information, answer th...
Concept:
If a random sample of size n is taken from a population with mean μ and s.d. σ, then the sample distribution of X (sample mean) has a mean equal to population mean i.e., μ and a s.d. σM
Therefore,  follows standard normal distribution.
Calculation:
We have μ = 98.6, σM=2.86
⇒ - 2.3 < Z < 1.19
= P(- 2.3 < Z < 1.19)
= FZ(1.19) − FZ(−2.3)
= 0.4843 + 0.3830
= 0.8723
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Most Upvoted Answer
Comprehension:Direction: Based on the following information, answer th...
Concept:
If a random sample of size n is taken from a population with mean μ and s.d. σ, then the sample distribution of X (sample mean) has a mean equal to population mean i.e., μ and a s.d. σM
Therefore,  follows standard normal distribution.
Calculation:
We have μ = 98.6, σM=2.86
⇒ - 2.3 < Z < 1.19
= P(- 2.3 < Z < 1.19)
= FZ(1.19) − FZ(−2.3)
= 0.4843 + 0.3830
= 0.8723
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Directions:Read the passages and choose the best answer to each question.PassageStudents debate 4 hypotheses regarding the origin of the asteroid belt located between Mars and Jupiter, based on the following observations.ObservationsObservation 1- If all of the asteroids were gathered together into one object, the diameter of the object formed would be less than half the diameter of Earth’s Moon.Observation 2- The total mass of the asteroid belt is only 4% that of the Moon. One asteroid alone, Ceres, contains 1/3 of the total mass of the asteroid belt.Observation 3- Asteroids are largely composed of silicate, with some deposits of iron and nickel, a composition proportionately similar to that of the terrestrial planets.Some asteroids also contain carbon and other elements.Observation 4- There is a strong orbital resonance (overlapping gravity) with Jupiter in the region of the asteroid belt, which keeps the asteroids in an orbit around the sun.Observation 5- In reality, asteroids within the belt are very far apart, not clustered together.Observation 6- Within the early solar system, the velocity of collisions within the region of the asteroid belt was much higher than it is currently.Hypothesis 1All of the material that makes up the asteroids in the asteroid belt is similar to that of the material that makes up the terrestrial planets. The velocity of collisions in the early solar system was at one time high enough to break apart planets as they formed. Since one asteroid, Ceres, has 1/3 the total mass of the belt, the asteroids are most likely the result of a partially formed planet that broke apart and became trapped in an orbit between Mars and Jupiter.Hypothesis 2 The material that composes the asteroids is similar to that of the terrestrial planets. The belt likely formed during the same time that the planets were forming, and due to the strong orbital resonance with the gas giant Jupiter and high velocity collisions, chunks of the material were pulled away from various planets and trapped within orbit. This also explains the varying composition of the asteroids throughout the belt.Hypothesis 3 The asteroids could not once have been a planet, because there is not enough material within the entire belt to form a planet-sized object. The lack of material, shown by the total diameter and mass of the objects within the belt, is proof that the asteroids are no more than large particles left over from the formation of the terrestrial planets from a single cloud of material.Hypothesis 4 The asteroids most likely came from somewhere outside the solar system. As they passed through space at varying intervals, they were trapped by the large orbital resonance of Jupiter and formed a “belt.” The vast distances between most of the asteroids in the belt are evidence that they did not come from a singular source, but arrived at different points in the belt’s development.Q.Consider the crust of a terrestrial planet to have a proportion of silicate to iron to nickel of 10,000:100:10.Based on the information in the passage, the ratio of these substances in the composition of an average asteroid is likely to be

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Comprehension:Direction: Based on the following information, answer the questions.For an experiment,a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:Find the corresponding probability given a sample of 36a)0.8723b)0.8c)0.745d)0.8892Correct answer is option 'A'. Can you explain this answer?
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Comprehension:Direction: Based on the following information, answer the questions.For an experiment,a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:Find the corresponding probability given a sample of 36a)0.8723b)0.8c)0.745d)0.8892Correct answer is option 'A'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Comprehension:Direction: Based on the following information, answer the questions.For an experiment,a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:Find the corresponding probability given a sample of 36a)0.8723b)0.8c)0.745d)0.8892Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Comprehension:Direction: Based on the following information, answer the questions.For an experiment,a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:Find the corresponding probability given a sample of 36a)0.8723b)0.8c)0.745d)0.8892Correct answer is option 'A'. Can you explain this answer?.
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