A machine produces widgets with a defect rate of 5%. What is the probability that a batch of 20 widgets will contain exactly 2 defective ones?
0.8113
0.1887
0.9975
0.0025
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?
50%
10%
Cannot be determined
6%
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 first 500 tosses will have more tails than heads.
The proportion of heads will be exactly 0.5.
The proportion of heads will be closer to 0.5 than if the coin were tossed only 10 times.
The number of heads will be exactly 500.
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?
$20
$2
$10
$4
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?
5/28
1/2
15/56
3/28
If two random variables X and Y are independent, what can be said about their joint probability distribution?
It cannot be determined from their marginal distributions.
It is equal to the sum of their marginal distributions.
It is always a uniform distribution.
It is equal to the product of their marginal distributions.
Suppose a diagnostic test for a certain disease has a 95% sensitivity and 90% specificity. It means that the test correctly identifies 95% of people with the disease and correctly identifies 90% of people without the disease. If the prevalence of the disease in a population is 1%, what is the probability that a person who tests positive actually has the disease?
0.500
0.095
0.086
0.090
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 bag contains 5 red balls and 3 blue balls. Two balls are drawn randomly without replacement. What is the probability that the second ball drawn is red, given that the first ball drawn was blue?
3/8
5/8
5/7
2/7
You roll two six-sided dice. Are the events "getting a sum of 7" and "getting doubles" independent events?
Yes
No