,1. Multiple Choice: If a set of data is normally distributed with a
mean of 50 and a standard deviation of 5, what is the probability
that a randomly selected score is between 45 and 55?
- A) 68%
- B) 95%
- C) 99.7%
- D) 50%
Correct Answer: A) 68%
Rationale: According to the empirical rule, approximately 68% of
the data within a normal distribution lies within one standard
deviation of the mean.
2. Fill-in-the-Blank: In a binomial distribution with n trials and a
probability of success p, the mean (expected value) is given by
_______.
Correct Answer: n*p
Rationale: The mean of a binomial distribution is found by
multiplying the number of trials by the probability of success.
, Correct Answer: True
Rationale: The Central Limit Theorem indeed states that, given a
sufficiently large sample size, the sampling distribution of the
sample mean will be approximately normal, regardless of the
population distribution's shape.
4. Multiple Response: Which of the following are properties of the
t-distribution?
- A) Symmetrical
- B) Has a mean of 0
- C) Has a standard deviation greater than 1
- D) Becomes more like the standard normal distribution as
sample size increases
Correct Answers: A) Symmetrical, B) Has a mean of 0, D)
Becomes more like the standard normal distribution as sample size
increases
Rationale: The t-distribution is symmetrical around a mean of 0,
and as the sample size increases, it approaches the standard normal
distribution. Its standard deviation is not fixed at greater than 1; it
varies depending on the degrees of freedom.
5. Multiple Choice: In a hypothesis test, if the p-value is less than
the significance level α, we:
- A) Reject the null hypothesis
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