The Normal Distributions Test (2024)

Table of Contents

What is the area under a standard normal curve? Another name for normal distribution is... In a normal distribution, the mean, mode and median are all equal. On which of the following is the shape of a normal distribution curve dependent on? What is the value of the constant e in normal distribution? What is the value of mode in standard normal distribution? About which of the following is a normal distribution symmetric? The standard normal curve is symmetrical about the value of... What is the skewness of normal distribution? What is the value of median in a standard normal distribution? References

1.
What is the area under a standard normal curve?
- A.
  1
- B.
- C.
  Not defined
- D.
  Infinity
Correct Answer
A. 1
Explanation
The area under a standard normal curve is 1. This is because a standard normal curve represents a normal distribution with a mean of 0 and a standard deviation of 1. The total area under the curve represents the probability of all possible outcomes, and since the total probability of all outcomes is 1, the area under the curve must also be 1.
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2.
Another name for normal distribution is...
- A.
  Lagrangian distribution
- B.
  Gaussian distribution
- C.
  Laplacian distribution
- D.
  Cauchy's distribution
Correct Answer
B. Gaussian distribution
Explanation
The correct answer is Gaussian distribution. The normal distribution is often referred to as the Gaussian distribution, named after the mathematician Carl Friedrich Gauss. It is a continuous probability distribution that is symmetrical and bell-shaped, with the majority of the data points falling near the mean. The Gaussian distribution is widely used in statistics and various fields to model and analyze random variables.
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3.
In a normal distribution, the mean, mode and median are all equal.
- A.
  True
- B.
  False
- C.
  See Also
  The Ultimate Normal Distribution Quiz The Normal Distribution, Revisited - AP Stats Study Guide 2024 | Fiveable
  Depends on the type of normal distribution
- D.
  Depends on some other factors
Correct Answer
A. True
Explanation
In a normal distribution, the mean, mode, and median are all equal because the normal distribution is symmetric. The mean represents the average value, the mode represents the most frequent value, and the median represents the middle value. In a symmetric distribution like the normal distribution, these three measures of central tendency coincide and have the same value. Therefore, the statement is true.
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4.
On which of the following is the shape of a normal distribution curve dependent on?
- A.
  Mean
- B.
  Variance
- C.
  Standard deviation
- D.
  Mean deviation
Correct Answer
A. Mean
Explanation
The shape of a normal distribution curve is dependent on the mean. The mean represents the average value of the data set and determines the center point of the distribution. It indicates where the peak of the curve will be located. A change in the mean will shift the entire curve either to the left or right, affecting the symmetry and position of the distribution. The variance, standard deviation, and mean deviation are measures of dispersion and do not directly impact the shape of the curve.
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21
5.
What is the value of the constant e in normal distribution?
- A.
  2.4183
- B.
  2.5183
- C.
  2.6183
- D.
  2.7183
Correct Answer
D. 2.7183
Explanation
The value of the constant e in normal distribution is 2.7183.
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6.
What is the value of mode in standard normal distribution?
- A.
  1
- B.
- C.
  Not fixed
- D.
  None
Correct Answer
B. 0
Explanation
In a standard normal distribution, the mode refers to the value that occurs most frequently. In this case, the mode is 0, meaning that 0 is the most common value in the distribution.
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7.
About which of the following is a normal distribution symmetric?
- A.
  Covariance
- B.
  Standard deviation
- C.
  Mean
- D.
  Variance
Correct Answer
C. Mean
Explanation
A normal distribution is symmetric, meaning that it is evenly distributed around its mean. The mean represents the center of the distribution, and the values on either side of the mean are equal. This symmetry is a characteristic of a normal distribution, making the mean the correct answer. Covariance, standard deviation, and variance are not necessarily symmetric and do not represent the center of a distribution.
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8.
The standard normal curve is symmetrical about the value of...
- A.
  1
- B.
- C.
  2
- D.
  4
Correct Answer
B. 0
Explanation
The standard normal curve is symmetrical about the value of 0 because the mean of a standard normal distribution is 0. This means that the curve is equally likely to be above or below 0, resulting in a symmetrical shape.
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9.
What is the skewness of normal distribution?
- A.
  1
- B.
  Undefined
- C.
  Positive
- D.
  Negative
Correct Answer
A. 1
Explanation
The skewness of a normal distribution is always 0. A normal distribution is symmetric, meaning it has equal amounts of data on both sides of the mean. This symmetry results in a skewness of 0. Therefore, the correct answer is 1, which represents undefined, is incorrect.
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01
10.
What is the value of median in a standard normal distribution?
- A.
  Infinity
- B.
  Not fixed
- C.
  1
- D.
Correct Answer
D. 0
Explanation
The value of the median in a standard normal distribution is 0. In a standard normal distribution, the mean is 0 and the standard deviation is 1. The distribution is symmetric, with half of the values falling below 0 and half above 0. Therefore, the median, which represents the middle value, is 0.
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