C280 Probability and Statistics I
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Free C280 Probability and Statistics I Questions
1. 2. In a normal distribution, approximately what percentage of data values lie within one standard deviation of the mean?
- A) 68%
- B) 75%
- C) 95%
- D) 99.7%
Explanation
In a standard normal distribution, the empirical rule (68-95-99.7 rule) states that about 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three. This rule helps in understanding the spread and variability of data, which is essential when interpreting data dispersion and probability in bell-shaped distributions.
2. 87. What is the complement of event A if P(A) = 0.65?
- A) 0.25
- B) 0.35
- C) 0.45
- D) 0.5
Explanation
The complement of event A represents the probability that A does not occur and is found by subtracting P(A) from 1. P(A′) = 1 – 0.65 = 0.35. Complementary probabilities always add up to 1.
3. 43. If the mean of five numbers is 12, what is the total sum of the numbers?
- A) 24
- B) 48
- C) 60
- D) 72
Explanation
The mean equals the total sum divided by the number of data points. Mean = Sum ÷ Number of values → 12 = Sum ÷ 5 → Sum = 12 × 5 = 60. Thus, the total of all five numbers must be 60.
4. 93. Which of the following would cause the range of a data set to increase?
- A) Adding a value near the mean
- B) Removing an outlier
- C) Adding a new extreme value
- D) Reducing the largest number
Explanation
The range depends on the difference between the largest and smallest values. Adding a new extreme (either very high or low) value increases that difference, thereby increasing the range and overall variability in the data.
5. 74. Which of the following best describes conditional probability?
- A) The probability of one event occurring regardless of another
- B) The probability of one event given that another has already occurred
- C) The probability of all events happening together
- D) The probability that an event is impossible
Explanation
Conditional probability measures the likelihood of one event occurring when another is known to have occurred. It’s expressed as P(A|B), read “the probability of A given B.” It’s key to understanding dependent events in real-world contexts like testing and quality control.
6. 22. If a data set has a mean of 50 and a standard deviation of 5, what is the z-score of a value equal to 60?
- A) 1
- B) 2
- C) -2
- D) -1
Explanation
The z-score formula is z = (x – μ) / σ. Here, z = (60 – 50) / 5 = 10 / 5 = 2. A z-score of 2 means the value is two standard deviations above the mean, indicating it is higher than most data points in a normal distribution.
7. 84. When data points fall closely along a straight line in a scatterplot, the correlation between the variables is:
- A) Weak
- B) Strong
- C) Nonexistent
- D) Negative
Explanation
A strong correlation exists when data points cluster tightly around a straight line, indicating a consistent linear relationship between variables. The closer the correlation coefficient (r) is to ±1, the stronger the relationship.
8. 48. If 15% of a store’s 400 customers buy gift cards, how many customers purchase them?
- A) 45
- B) 50
- C) 60
- D) 75
Explanation
To find 15% of 400: 0.15 × 400 = 60. Percentage calculations are used frequently in descriptive statistics, finance, and business decision-making to represent proportions.
9. 37. A data set contains values: 5, 7, 7, 8, 9, 10, and 15. Which measure of central tendency best represents the data?
- A) Mean
- B) Median
- C) Mode
- D) Range
Explanation
The median is the middle value when the data are ordered, and it’s less affected by outliers such as 15. Here, the median (8) provides a more accurate representation of central tendency than the mean, which would be skewed higher due to the large outlier.
10. 6. A student rolls a fair six-sided die. What is the probability of rolling an even number?
- A) 1/6
- B) 1/3
- C) 1/2
- D) 2/3
Explanation
The even numbers on a six-sided die are 2, 4, and 6. Since there are three favorable outcomes out of six possible outcomes, the probability equals 3/6, which simplifies to 1/2. This shows that the likelihood of rolling an even number is 50%.
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