The time until a radioactive particle decays is modeled by an exponential distribution. If the average decay time is 10 seconds, what is the median decay time?
10 seconds
5 seconds
6.93 seconds
14.43 seconds
In a dataset of customer purchase history, what kind of analysis would likely involve using joint and conditional probability distributions?
Predicting the probability of a customer purchasing product B given they purchased product A
Calculating the average purchase amount
Visualizing the distribution of customer ages
Identifying the most frequent purchase day of the week
A fair coin is tossed 1000 times. According to the Law of Large Numbers, which of the following statements is MOST likely to be true?
The proportion of heads will be exactly 0.5.
The number of heads will be exactly 500.
The first 500 tosses will have more tails than heads.
The proportion of heads will be closer to 0.5 than if the coin were tossed only 10 times.
The lifetime of a certain battery follows a gamma distribution with a shape parameter of 2 and a scale parameter of 500 hours. What is the average lifetime of this battery?
250 hours
2000 hours
500 hours
1000 hours
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 this only describes a conditional probability, not the reverse.
Yes, because the probabilities must be equal.
Yes, because buying product B makes it more likely someone buys product A.
No, because the probabilities are independent of each other.
In a certain city, 70% of the population owns a car and 40% owns a bike. Among the car owners, 30% also own a bike. If a person is randomly selected from the city, what is the probability that they own both a car and a bike?
0.58
0.21
0.28
0.12
If the time to complete a task is exponentially distributed with a mean of 20 minutes, what is the probability that the task takes less than 10 minutes?
0.393
0.607
0.368
0.632
A machine produces bolts with diameters that are normally distributed with a mean of 4mm and a standard deviation of 0.1mm. What percentage of bolts will have a diameter between 3.8mm and 4.2mm?
99.73%
95.45%
50%
68.27%
Events A and B are independent. The probability of A occurring is 0.4, and the probability of B occurring is 0.6. What is the probability that at least one of the events, A or B, will occur?
0.24
0.50
0.76
1.00
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
0.0228