The weight of a bag of chips is normally distributed with a mean of 250 grams and a standard deviation of 5 grams. If a bag is selected at random, what is the probability that it weighs less than 240 grams?
0.9772
0.0228
0.5
0.4772
What is a key difference between the Weak Law of Large Numbers and the Strong Law of Large Numbers?
The Weak Law deals with the convergence in probability, while the Strong Law deals with almost sure convergence.
The Weak Law applies only to discrete distributions, while the Strong Law applies to both discrete and continuous distributions.
The Weak Law is used in hypothesis testing, while the Strong Law is used in confidence interval estimation.
The Weak Law considers a finite number of trials, while the Strong Law considers an infinite number of trials.
In a dataset of customer purchase history, what kind of analysis would likely involve using joint and conditional probability distributions?
Visualizing the distribution of customer ages
Identifying the most frequent purchase day of the week
Predicting the probability of a customer purchasing product B given they purchased product A
Calculating the average purchase amount
A company produces light bulbs with a lifespan that is skewed to the right. The average lifespan is 1000 hours with a standard deviation of 100 hours. If you randomly select 100 light bulbs, what is the approximate probability that their average lifespan is greater than 1010 hours?
0.8413
0.1587
0.3085
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 data must be normally distributed.
The population standard deviation needs to be known or estimated.
The samples should be independent of each other.
How is the marginal probability distribution of X obtained from the joint probability distribution of X and Y?
By multiplying the joint probabilities by the marginal probabilities of Y
By subtracting the joint probabilities from 1
By dividing the joint probabilities by the marginal probabilities of Y
By summing the joint probabilities over all possible values of Y
A bag contains 5 red balls and 3 blue balls. Two balls are drawn one after another without replacement. What is the probability that the first ball is red and the second ball is blue?
15/56
3/28
5/28
1/2
A study shows that 60% of people who buy product A also buy product B. Is it necessarily true that 60% of people who buy product B also buy product A?
Yes, because buying product B makes it more likely someone buys product A.
Yes, because the probabilities must be equal.
No, because the probabilities are independent of each other.
No, because this only describes a conditional probability, not the reverse.
In a large dataset of customer purchase amounts, the average purchase is $50 with a standard deviation of $20. If we take 100 random samples of size 25 from this dataset, what will be the standard deviation of the distribution of these sample means?
$2
$20
$4
$10
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 identical to the distribution of individual tree heights.
The Central Limit Theorem cannot be applied to this situation.
The distribution of sample means will be approximately normal.
The distribution of sample means will be skewed right.