60 Quiz 2.2 A Ap Statistics Answers
Introduction
Welcome to our comprehensive guide to the Quiz 2.2 A AP Statistics answers! In this article, we will walk you through the solutions to the questions in Quiz 2.2 A of the AP Statistics course. This quiz is designed to test your understanding of probability and the normal distribution, two fundamental concepts in statistics. By going through the answers and explanations provided here, you will be able to reinforce your knowledge and improve your ability to tackle similar questions in the future.
Question 1: Probability
To begin, let's take a look at the first question on the quiz, which focuses on probability. The question states:
"A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is selected at random, what is the probability that it will be blue?"
The key to solving this question is to understand that the probability of an event occurring is equal to the number of favorable outcomes divided by the total number of possible outcomes. In this case, there are 3 blue marbles out of a total of 10 marbles in the bag, so the probability is 3/10 or 0.3.
Therefore, the answer to question 1 is 0.3.
Question 2: Normal Distribution
Next, let's move on to the second question, which pertains to the normal distribution. The question reads:
"The heights of adult males in a certain population are normally distributed with a mean of 68 inches and a standard deviation of 3 inches. What is the probability that a randomly selected adult male will have a height greater than 72 inches?"
To solve this question, we need to use the concept of z-scores. A z-score measures the number of standard deviations a data point is from the mean. In this case, we want to find the probability of selecting a male with a height greater than 72 inches, which is 4 inches above the mean. By calculating the z-score, we can then look up the corresponding probability in a standard normal distribution table.
The formula for calculating the z-score is:
z = (x - μ) / σ
where z is the z-score, x is the data point, μ is the mean, and σ is the standard deviation.
Plugging in the values from the question, we have:
z = (72 - 68) / 3 = 4 / 3 = 1.33
Using a standard normal distribution table, we can find that the probability of a z-score greater than 1.33 is approximately 0.0918.
Therefore, the answer to question 2 is approximately 0.0918.
Question 3: Probability and Combinations
Now, let's move on to the third question, which combines probability and combinations. The question states:
"A committee of 4 people is to be selected from a group of 10 individuals. How many different committees can be formed?"
To solve this question, we need to use the concept of combinations. The formula for calculating the number of combinations is:
nCr = n! / (r!(n-r)!)
where n is the total number of items, r is the number of items to be chosen, and ! denotes factorial (the product of all positive integers up to a given number).
In this case, we have 10 individuals and we want to choose 4 people for the committee. Plugging in the values, we have:
10C4 = 10! / (4!(10-4)!) = 10! / (4!6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210
Therefore, the answer to question 3 is 210.
Question 4: Probability and Percentiles
Lastly, let's tackle the fourth question, which involves probability and percentiles. The question reads:
"The scores on a standardized test are normally distributed with a mean of 75 and a standard deviation of 10. What is the minimum score needed to be in the top 10% of test takers?"
To solve this question, we need to find the z-score corresponding to the 90th percentile (since we want to be in the top 10%). Using a standard normal distribution table, we can find that the z-score corresponding to the 90th percentile is approximately 1.28.
The formula for calculating the minimum score needed is:
x = μ + (z * σ)
where x is the minimum score needed, μ is the mean, z is the z-score, and σ is the standard deviation.
Plugging in the values, we have:
x = 75 + (1.28 * 10) = 75 + 12.8 = 87.8
Therefore, the answer to question 4 is approximately 87.8.
Conclusion
Congratulations on completing the Quiz 2.2 A AP Statistics answers guide! By going through the solutions and explanations provided, you have reinforced your understanding of probability, the normal distribution, combinations, and percentiles. Remember to practice these concepts regularly to further enhance your statistical skills. Good luck with your future studies!