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 samples should be independent of each other.
The population standard deviation needs to be known or estimated.
You're a data scientist analyzing website traffic. You have data on the average time users spend on a page, which is 2 minutes with a standard deviation of 30 seconds. You want to estimate the probability that the average time spent on the page by a random sample of 100 users is between 1 minute 55 seconds and 2 minutes 5 seconds. What concept would be most suitable for this calculation?
Conditional Probability
Central Limit Theorem
Bayes' Theorem
Law of Large Numbers
A box contains 4 red balls and 6 green balls. Two balls are drawn consecutively without replacement. What is the probability that both balls are red?
4/25
2/15
1/6
8/15
A machine produces bolts with diameters normally distributed, a mean of 10mm, and a standard deviation of 0.2mm. What percentage of bolts will have a diameter between 9.7mm and 10.3mm?
95.45%
86.64%
99.73%
68.27%
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?
0.3085
0.8413
0.0228
0.1587
What is a key difference between the Weak Law of Large Numbers and the Strong Law of Large Numbers?
The Weak Law applies only to discrete distributions, while the Strong Law applies to both discrete and continuous distributions.
The Weak Law considers a finite number of trials, while the Strong Law considers an infinite number of trials.
The Weak Law is used in hypothesis testing, while the Strong Law is used in confidence interval estimation.
The Weak Law deals with the convergence in probability, while the Strong Law deals with almost sure convergence.
The weight of apples is normally distributed with a mean of 150g and a standard deviation of 10g. What is the z-score for an apple weighing 165g?
1.5
-0.67
0.67
-1.5
A box contains 4 green marbles and 6 red marbles. Two marbles are drawn one after the other without replacement. What is the probability that the first marble is green and the second is red?
4/15
6/25
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?
$4
$2
$20
$10
In a dataset of customer purchase history, what kind of analysis would likely involve using joint and conditional probability distributions?
Identifying the most frequent purchase day of the week
Calculating the average purchase amount
Visualizing the distribution of customer ages
Predicting the probability of a customer purchasing product B given they purchased product A