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An unbiased die is tossed 500 times. The Standard deviation of the no. of ‘sixes’ in these 500 tossed is
- a)50/6
- b)500/6
- c)5/6
- d)none
Correct answer is option 'A'. Can you explain this answer?
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An unbiased die is tossed 500 times. The Standard deviation of the no....
Given information
- An unbiased die is tossed 500 times.
- We need to find the standard deviation of the number of sixes in these 500 tosses.
Approach
- We can find the standard deviation using the formula for a binomial distribution.
- In a binomial distribution, the probability of success (getting a six) is p = 1/6, and the probability of failure (not getting a six) is q = 5/6.
- The mean of a binomial distribution is np, where n is the number of trials and p is the probability of success.
- The variance of a binomial distribution is npq.
- The standard deviation is the square root of the variance.
Calculations
- n = 500 (number of trials)
- p = 1/6 (probability of success)
- q = 5/6 (probability of failure)
- Mean = np = 500 * 1/6 = 83.33
- Variance = npq = 500 * 1/6 * 5/6 = 69.44
- Standard deviation = square root of variance = sqrt(69.44) = 8.33
Answer
- The standard deviation of the number of sixes in 500 tosses of an unbiased die is 8.33.
- Option A (50/6) is the closest answer to the calculated standard deviation (8.33).
- An unbiased die is tossed 500 times.
- We need to find the standard deviation of the number of sixes in these 500 tosses.
Approach
- We can find the standard deviation using the formula for a binomial distribution.
- In a binomial distribution, the probability of success (getting a six) is p = 1/6, and the probability of failure (not getting a six) is q = 5/6.
- The mean of a binomial distribution is np, where n is the number of trials and p is the probability of success.
- The variance of a binomial distribution is npq.
- The standard deviation is the square root of the variance.
Calculations
- n = 500 (number of trials)
- p = 1/6 (probability of success)
- q = 5/6 (probability of failure)
- Mean = np = 500 * 1/6 = 83.33
- Variance = npq = 500 * 1/6 * 5/6 = 69.44
- Standard deviation = square root of variance = sqrt(69.44) = 8.33
Answer
- The standard deviation of the number of sixes in 500 tosses of an unbiased die is 8.33.
- Option A (50/6) is the closest answer to the calculated standard deviation (8.33).
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An unbiased die is tossed 500 times. The Standard deviation of the no. of ‘sixes’ in these 500 tossed isa)50/6b)500/6c)5/6d)noneCorrect answer is option 'A'. Can you explain this answer?
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