A company wants to analyze its website traffic. The time a user spends on the website follows a gamma distribution. Which of these is NOT a suitable use of the gamma distribution in this scenario?
Modeling the total time users spend on specific pages.
Predicting the time until a user makes a purchase.
Estimating the probability of a user clicking on an advertisement.
Analyzing the distribution of session durations.
The amount of time a customer spends waiting in line at a bank is modeled by a gamma distribution with a shape parameter of 2 and a rate parameter of 0.5. What is the expected waiting time for a customer?
4 minutes
1 minute
2 minutes
0.25 minutes
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
A casino owner wants to ensure that their roulette wheel is fair. How could they apply the Law of Large Numbers to test this?
Use computer simulations to predict the outcomes of roulette spins and compare them to real-world results.
Hire a mathematician to calculate the exact probability of each outcome on the roulette wheel.
Spin the wheel thousands of times and record the results. The distribution of outcomes should be close to the theoretical probabilities.
Spin the wheel a small number of times and analyze the results for any obvious patterns.
A company's daily stock price fluctuations are approximately normally distributed with a mean of $0 (no change) and a standard deviation of $2. What is the probability that the stock price will increase by more than $4 on a given day?
0.9772
0.8413
0.1587
0.0228
A bag contains 5 red marbles and 5 blue marbles. You draw two marbles from the bag without replacement. What is the probability that both marbles are red?
1/4
2/9
1/2
1/9
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?
No, because the probabilities are independent of each other.
Yes, because buying product B makes it more likely someone buys product A.
Yes, because the probabilities must be equal.
No, because this only describes a conditional probability, not the reverse.
You roll two six-sided dice. Are the events "getting a sum of 7" and "getting doubles" independent events?
No
Yes
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?
0.4772
0.5
Suppose 30% of people in a city own a car and 20% own a bicycle. If car ownership and bicycle ownership are independent, what is the probability that a randomly selected person owns both a car and a bicycle?
10%
Cannot be determined
50%
6%