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Let X denote the number of scores which exceed 4 in 18, tosses of a symmetrical die. Consider the following statements:
1. The arithmetic mean o f X is 6.
2. The standard deviation ofX is 2.
Which of the above statements is/are correct ?
  • a)
    1 only
  • b)
    2 only
  • c)
    Both 1 and 2
  • d)
    Neither 1 nor 2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let X denote the number of scores which exceed 4 in 18, tosses of a sy...
Statement 1 :
n (X) = 2

arithmetric mean of X = np

Statement 2: Standard deviation of 


Hence, statements 1 and 2 both are correct. 
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Most Upvoted Answer
Let X denote the number of scores which exceed 4 in 18, tosses of a sy...
Solution:

Given, X denotes the number of scores which exceed 4 in 18 tosses of a symmetrical die.

Let p be the probability of getting a score greater than 4 in a single toss of the die. Then,

p = P(score > 4) = 2/6 = 1/3

q = 1 - p = P(score ≤ 4) = 4/6 = 2/3

1. Mean of X
The number of scores greater than 4 in 18 tosses of the die follows a binomial distribution with parameters n = 18 and p = 1/3. The mean of this distribution is given by:

μ = np = 18 × (1/3) = 6

Therefore, statement 1 is correct.

2. Standard deviation of X
The standard deviation of a binomial distribution with parameters n and p is given by:

σ = √(npq)

Substituting n = 18, p = 1/3 and q = 2/3, we get:

σ = √(18 × 1/3 × 2/3) = √4 = 2

Therefore, statement 2 is also correct.

Hence, both statements 1 and 2 are correct, and the answer is option (c).
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Let X denote the number of scores which exceed 4 in 18, tosses of a symmetrical die. Consider the following statements:1. The arithmetic mean o f X is 6.2. The standard deviation ofX is 2.Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. Can you explain this answer?
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Let X denote the number of scores which exceed 4 in 18, tosses of a symmetrical die. Consider the following statements:1. The arithmetic mean o f X is 6.2. The standard deviation ofX is 2.Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Let X denote the number of scores which exceed 4 in 18, tosses of a symmetrical die. Consider the following statements:1. The arithmetic mean o f X is 6.2. The standard deviation ofX is 2.Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X denote the number of scores which exceed 4 in 18, tosses of a symmetrical die. Consider the following statements:1. The arithmetic mean o f X is 6.2. The standard deviation ofX is 2.Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. Can you explain this answer?.
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