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?
0.0228
0.5
0.4772
0.9772
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 summing the joint probabilities over all possible values of Y
By dividing the joint probabilities by the marginal probabilities of Y
By subtracting the joint probabilities from 1
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 fair coin is flipped three times. What is the probability of getting at least two heads?
1/2
1/8
3/4
1/4
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?
-0.67
0.67
1.5
-1.5
A casino owner wants to ensure that their roulette wheel is fair. How could they apply the Law of Large Numbers to test this?
Spin the wheel a small number of times and analyze the results for any obvious patterns.
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.
Use computer simulations to predict the outcomes of roulette spins and compare them to real-world results.
The lifetime of a certain component follows a gamma distribution with a shape parameter of 3 and a rate parameter of 0.2. What is the variance of the component's lifetime?
45
15
7.5
75
The time (in minutes) between customer arrivals at a bank is exponentially distributed with an average of 5 minutes. What is the probability a customer arrives within 3 minutes of the previous customer?
0.549
0.368
0.632
0.451
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
5/28
3/28
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?
6/25
4/15
1/6
2/15