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The interval (µ - 3σ, µ + 3σ) covers
- a)95% area of a normal distribution.
- b)96% area of a normal distribution.
- c)99% area of a normal distribution.
- d)all but 0.27% area of a normal distribution.
Correct answer is option 'D'. Can you explain this answer?
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The interval (µ - 3σ, µ + 3σ) coversa)95% area of ...
Normal Distribution and Interval
The normal distribution is a bell-shaped curve that represents the distribution of many variables in the real world. It is a continuous probability distribution that is symmetrical around the mean. The area under the curve represents the probability of a particular event occurring.
In statistics, an interval is a range of values that is defined by two numbers, usually representing the lower and upper limits of the range. For example, the interval ( - 3, 3) represents all the values between -3 and 3, including -3 and 3.
Calculating the Area Under the Curve
To calculate the area under the curve for a normal distribution, we need to know two things: the mean and the standard deviation. The mean represents the center of the distribution, while the standard deviation represents the spread of the distribution.
The area under the curve between two values can be calculated using a table or a calculator that is programmed to perform the calculation. For example, the area under the curve between -1 and 1 for a standard normal distribution (mean = 0, standard deviation = 1) is approximately 0.68.
Answer Explanation
The interval ( - 3, 3) covers all but 0.27% area of a normal distribution. This means that 99.73% of the area is covered by this interval. This is because the interval represents three standard deviations from the mean, which covers almost all of the area under the curve for a normal distribution.
Therefore, the correct answer is option 'D' - all but 0.27% area of a normal distribution.
The normal distribution is a bell-shaped curve that represents the distribution of many variables in the real world. It is a continuous probability distribution that is symmetrical around the mean. The area under the curve represents the probability of a particular event occurring.
In statistics, an interval is a range of values that is defined by two numbers, usually representing the lower and upper limits of the range. For example, the interval ( - 3, 3) represents all the values between -3 and 3, including -3 and 3.
Calculating the Area Under the Curve
To calculate the area under the curve for a normal distribution, we need to know two things: the mean and the standard deviation. The mean represents the center of the distribution, while the standard deviation represents the spread of the distribution.
The area under the curve between two values can be calculated using a table or a calculator that is programmed to perform the calculation. For example, the area under the curve between -1 and 1 for a standard normal distribution (mean = 0, standard deviation = 1) is approximately 0.68.
Answer Explanation
The interval ( - 3, 3) covers all but 0.27% area of a normal distribution. This means that 99.73% of the area is covered by this interval. This is because the interval represents three standard deviations from the mean, which covers almost all of the area under the curve for a normal distribution.
Therefore, the correct answer is option 'D' - all but 0.27% area of a normal distribution.
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The interval (µ - 3σ, µ + 3σ) coversa)95% area of a normal distribution.b)96% area of a normal distribution.c)99% area of a normal distribution.d)all but 0.27% area of a normal distribution.Correct answer is option 'D'. Can you explain this answer?
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