In a normal distribution, what percentage of data falls within three standard deviations of the mean?
68.27%
99.73%
100%
95.45%
A fair coin is flipped three times. What is the probability of getting at least two heads?
1/4
3/4
1/8
1/2
You toss a fair coin twice. What is the probability of getting heads on the first toss and tails on the second toss?
1/3
1
In the context of machine learning, how does the Law of Large Numbers relate to training data?
A model trained on a larger, more representative dataset is likely to generalize better to unseen data.
The Law of Large Numbers is irrelevant to machine learning; it's a purely statistical concept.
The Law of Large Numbers dictates the optimal learning rate for a machine learning model.
It proves that a complex model will always outperform a simpler model given enough data.
Events A and B are independent. The probability of event A is 0.3. The probability of event B is 0.6. What is the probability of both A and B occurring?
0.90
Cannot be determined from the given information.
0.50
0.18
You have two standard decks of cards. You draw one card from each deck. What is the probability that both cards are Aces?
1/169
1/52
1/26
1/13
A machine produces widgets with a defect rate of 5%. What is the probability that a batch of 20 widgets will contain exactly 2 defective ones?
0.1887
0.9975
0.0025
0.8113
A spam filter correctly identifies 95% of spam emails. However, it also flags 2% of legitimate emails as spam. If 1% of all emails are actually spam, what is the probability that an email flagged as spam is actually spam?
95%
32%
50%
2%
You're analyzing the average height of trees in a forest. You take multiple samples of 50 trees each. According to the Central Limit Theorem, what can you infer about the distribution of the sample means of these tree heights?
The distribution of sample means will be skewed right.
The Central Limit Theorem cannot be applied to this situation.
The distribution of sample means will be identical to the distribution of individual tree heights.
The distribution of sample means will be approximately normal.
Which of the following is NOT an assumption or condition that should be met when applying the Central Limit Theorem?
The sample size should be sufficiently large (generally n ≥ 30).
The population standard deviation needs to be known or estimated.
The samples should be independent of each other.
The population data must be normally distributed.