1. What is the shape of a normal distribution curve?
Correct Answer: C) Bell-shaped
Explanation:
The normal distribution curve is symmetric and bell-shaped, with the highest point at the mean. This characteristic shape gives it the name "bell curve." The curve approaches but never touches the x-axis as it extends infinitely in both directions.
2. In a standard normal distribution, what is the mean (μ)?
Correct Answer: B) 0
Explanation:
The standard normal distribution is a special case of the normal distribution where the mean (μ) is 0 and the standard deviation (σ) is 1. This standardization allows for easier comparison between different normal distributions.
3. What percentage of data falls within one standard deviation (±1σ) in a normal distribution?
Correct Answer: B) 68%
Explanation:
This is part of the empirical rule (68-95-99.7 rule) which states that in a normal distribution:
≈68% of data falls within ±1 standard deviation of the mean,
≈95% within ±2 standard deviations,
≈99.7% within ±3 standard deviations.
4. The empirical rule states that approximately 99.7% of data falls within how many standard deviations from the mean?
Correct Answer: C) 3σ
Explanation:
The empirical rule specifies that in a normal distribution, about 99.7% of values lie within three standard deviations (3σ) of the mean. This means only about 0.3% of data points fall outside this range.
5. The standard deviation (σ) measures the _______ of the data.
Correct Answer: B) Spread
Explanation:
Standard deviation is a measure of how spread out the numbers in a data set are. A low standard deviation means most numbers are close to the mean, while a high standard deviation means the numbers are more spread out.
6. What happens when the standard deviation increases in a normal distribution?
Correct Answer: B) The curve becomes wider and flatter
Explanation:
As standard deviation increases, the spread of the data increases. This causes the normal curve to become wider and flatter because the data is more dispersed. Conversely, a smaller standard deviation makes the curve taller and narrower.
7. The total area under a normal distribution curve is always equal to:
Correct Answer: B) 1
Explanation:
The total area under any probability distribution curve, including the normal distribution, always equals 1 (or 100%). This represents the fact that all possible outcomes are accounted for within the distribution.
8. Which formula is used to compute the Z-score in a normal distribution?
Correct Answer: A) Z = (X - μ)/σ
Explanation:
The Z-score formula Z = (X - μ)/σ converts any normal distribution to the standard normal distribution (μ=0, σ=1). It tells us how many standard deviations a particular value (X) is from the mean (μ).
9. If a dataset has a mean of 50 and a standard deviation of 5, what is the Z-score for a value of 60?
Correct Answer: B) 2
Explanation:
Using the Z-score formula: Z = (X - μ)/σ = (60 - 50)/5 = 10/5 = 2. This means 60 is 2 standard deviations above the mean. Z-scores are particularly useful for comparing values from different normal distributions.
10. What does a Z-score of 0 indicate?
Correct Answer: C) The value is equal to the mean
Explanation:
A Z-score of 0 means the data point is exactly at the mean. This is because Z = (X - μ)/σ, so when X = μ, the numerator becomes 0, making the entire Z-score 0.
11. Which of the following statements about normal distribution is true?
Correct Answer: C) The curve extends infinitely in both directions
Explanation:
The normal distribution curve theoretically extends to infinity in both directions, never actually touching the x-axis. This is a mathematical idealization - in practice, most data falls within 3-4 standard deviations of the mean.
12. If a Z-score is negative, what does it mean?
Correct Answer: C) The value is less than the mean
Explanation:
A negative Z-score indicates the data point is below the mean. The sign of the Z-score tells us the direction from the mean (negative = below, positive = above), while the magnitude tells us how many standard deviations away it is.
13. Which of the following statements is true about a standard normal distribution?
Correct Answer: B) The standard deviation is always 1
Explanation:
By definition, a standard normal distribution has a mean (μ) of 0 and standard deviation (σ) of 1. This standardization allows for the creation of Z-tables and simplifies probability calculations.