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A binomial distribution is
- a)never symmetrical.
- b)never positively skewed.
- c)never negatively skewed.
- d)symmetrical when p = 0.5.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A binomial distribution isa)never symmetrical.b)never positively skewe...
Explanation:
Binomial distribution is a type of probability distribution that deals with the number of successes and failures in a fixed number of independent trials. It is defined by two parameters: n, the number of trials, and p, the probability of success in each trial.
Symmetry in Binomial Distribution:
When p = 0.5, the binomial distribution is symmetric. This is because when p = 0.5, the probability of success is equal to the probability of failure, and the outcomes are equally likely to occur. Therefore, the distribution is centered around the midpoint, and the shape of the distribution is symmetrical.
Skewness in Binomial Distribution:
Skewness is a measure of the asymmetry of a distribution. In a binomial distribution, skewness can occur when the probability of success is either very high or very low. If the probability of success is high, the distribution is positively skewed, and if the probability of success is low, the distribution is negatively skewed.
Conclusion:
In conclusion, the correct answer is option 'D.' Symmetry in a binomial distribution only occurs when p = 0.5, and it is never positively or negatively skewed.
Binomial distribution is a type of probability distribution that deals with the number of successes and failures in a fixed number of independent trials. It is defined by two parameters: n, the number of trials, and p, the probability of success in each trial.
Symmetry in Binomial Distribution:
When p = 0.5, the binomial distribution is symmetric. This is because when p = 0.5, the probability of success is equal to the probability of failure, and the outcomes are equally likely to occur. Therefore, the distribution is centered around the midpoint, and the shape of the distribution is symmetrical.
Skewness in Binomial Distribution:
Skewness is a measure of the asymmetry of a distribution. In a binomial distribution, skewness can occur when the probability of success is either very high or very low. If the probability of success is high, the distribution is positively skewed, and if the probability of success is low, the distribution is negatively skewed.
Conclusion:
In conclusion, the correct answer is option 'D.' Symmetry in a binomial distribution only occurs when p = 0.5, and it is never positively or negatively skewed.
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A binomial distribution isa)never symmetrical.b)never positively skewe...
A binomial distribution occurs when there are only two mutually exclusive possible outcomes, for example the outcome of tossing a coin is heads or tails. It is usual to refer to one outcome as "success" and the other outcome as "failure
The mean of a binomial distribution is p and its standard deviation is sqr(p(1-p)/n). The shape of a binomial distribution is symmetrical when p=0.5 or when n is large
The mean of a binomial distribution is p and its standard deviation is sqr(p(1-p)/n). The shape of a binomial distribution is symmetrical when p=0.5 or when n is large
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A binomial distribution isa)never symmetrical.b)never positively skewed.c)never negatively skewed.d)symmetrical when p = 0.5.Correct answer is option 'D'. Can you explain this answer?
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