when the sampling distribution of means is plotted which of the following is true

ATI TEAS 7

TEAS Test Math Prep

1. When the sampling distribution of means is plotted, which of the following is true?

A. The distribution is approximately normal.
B. The distribution is positively skewed.
C. The distribution is negatively skewed.
D. There is no predictable shape to the distribution.

Correct answer: A

Rationale: When the sampling distribution of means is plotted, the distribution tends to be approximately normal, especially as the sample size increases. This phenomenon is described by the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed regardless of the shape of the original population distribution as long as the sample size is sufficiently large. Choices B and C are incorrect because sampling distributions of means are not skewed. Choice D is incorrect because there is a predictable shape to the distribution, which is approximately normal.

2. What is the median of the set of numbers {2, 3, 9, 12, 15}?

A. 3
B. 9
C. 12
D. 15

Correct answer: B

Rationale: The median represents the middle value in an ordered set of numbers. To find the median, the numbers need to be arranged in ascending order: {2, 3, 9, 12, 15}. Since the set has an odd number of elements, the median will be the middle value, which is 9 in this case. Choice A (3) and Choice D (15) are incorrect as they do not fall in the middle of the ordered set. Choice C (12) is also incorrect as it is not the middle value in this particular set.

3. Out of 9 trips, a person chooses the longest route for 3 of them. What percentage of their trips is the longest route?

A. 0.25
B. 0.33
C. 0.5
D. 0.75

Correct answer: B

Rationale: To find the percentage of trips where the person chose the longest route, divide the number of longest route trips (3) by the total number of trips (9) and multiply by 100. This gives (3/9) * 100 = 33.33%, which can be rounded to 33%. Therefore, the correct answer is B. Choice A (0.25), C (0.5), and D (0.75) are incorrect because they do not accurately represent the percentage of trips where the longest route was chosen based on the given information.

4. What is the mode of the numbers in the distribution shown in the table?

A. 1
B. 2
C. 3
D. 4

Correct answer: A

Rationale: The mode of a set of numbers is the value that appears most frequently. In the distribution shown in the table, the number '1' occurs more times than any other number, making it the mode. Choices B, C, and D are incorrect because they do not represent the number that occurs most frequently in the dataset.

5. A closet is filled with red, blue, and green shirts. If 2/5 of the shirts are green and 1/3 are red, what fraction of the shirts are blue?

A. 4/15
B. 1/5
C. 7/15
D. 1/2

Correct answer: C

Rationale: To find the fraction of blue shirts, subtract the fractions of green and red shirts from 1. Green shirts are 2/5 and red shirts are 1/3, which sum up to 11/15. Therefore, blue shirts would be 1 - 11/15 = 4/15. So, the correct answer is 4/15. Choice A (4/15) is incorrect as it represents the overall fraction of green shirts. Choice B (1/5) is incorrect as it does not account for the fractions of green and red shirts. Choice D (1/2) is incorrect as it does not consider the given fractions of green and red shirts.