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Mathematical Modeling: Probability and Statistics

Description: This quiz will test your understanding of Mathematical Modeling: Probability and Statistics.
Number of Questions: 14
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Tags: probability statistics mathematical modeling
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What is the probability of getting a head when you flip a coin?

  1. 1/2

  2. 1/4

  3. 1/3

  4. 1/6


Correct Option: A
Explanation:

When you flip a coin, there are two possible outcomes: heads or tails. Since each outcome is equally likely, the probability of getting a head is 1/2.

What is the probability of getting a sum of 7 when you roll two dice?

  1. 1/6

  2. 1/12

  3. 1/18

  4. 1/24


Correct Option: A
Explanation:

There are 36 possible outcomes when you roll two dice. The outcomes that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). So, the probability of getting a sum of 7 is 6/36 = 1/6.

What is the mean of a normal distribution with a mean of 5 and a standard deviation of 2?

  1. 5

  2. 7

  3. 9

  4. 11


Correct Option: A
Explanation:

The mean of a normal distribution is the center of the distribution. In this case, the mean is 5.

What is the standard deviation of a normal distribution with a mean of 5 and a standard deviation of 2?

  1. 1

  2. 2

  3. 3

  4. 4


Correct Option: B
Explanation:

The standard deviation of a normal distribution is a measure of how spread out the distribution is. In this case, the standard deviation is 2.

What is the probability of getting a z-score of 1.96 or higher in a standard normal distribution?

  1. 0.025

  2. 0.05

  3. 0.01

  4. 0.005


Correct Option: A
Explanation:

The z-score of 1.96 corresponds to the 97.5th percentile in a standard normal distribution. So, the probability of getting a z-score of 1.96 or higher is 0.025.

What is the probability of getting a sample mean of 100 or higher from a population with a mean of 100 and a standard deviation of 10, if the sample size is 100?

  1. 0.5

  2. 0.68

  3. 0.95

  4. 0.99


Correct Option: D
Explanation:

The sampling distribution of the sample mean is a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the sampling distribution of the sample mean has a mean of 100 and a standard deviation of 10 / sqrt(100) = 1. So, the probability of getting a sample mean of 100 or higher is 0.99.

What is the probability of getting a sample proportion of 0.5 or higher from a population with a proportion of 0.5, if the sample size is 100?

  1. 0.5

  2. 0.68

  3. 0.95

  4. 0.99


Correct Option: D
Explanation:

The sampling distribution of the sample proportion is a normal distribution with a mean equal to the population proportion and a standard deviation equal to the square root of the population proportion times the square root of 1 minus the population proportion, divided by the square root of the sample size. In this case, the sampling distribution of the sample proportion has a mean of 0.5 and a standard deviation of sqrt(0.5 * 0.5) / sqrt(100) = 0.05. So, the probability of getting a sample proportion of 0.5 or higher is 0.99.

What is the probability of getting a chi-square statistic of 10 or higher from a chi-square distribution with 5 degrees of freedom?

  1. 0.05

  2. 0.10

  3. 0.15

  4. 0.20


Correct Option: A
Explanation:

The chi-square distribution with 5 degrees of freedom has a mean of 5 and a standard deviation of sqrt(2 * 5) = sqrt(10). So, the probability of getting a chi-square statistic of 10 or higher is 0.05.

What is the probability of getting a t-statistic of 2 or higher from a t-distribution with 10 degrees of freedom?

  1. 0.05

  2. 0.10

  3. 0.15

  4. 0.20


Correct Option: A
Explanation:

The t-distribution with 10 degrees of freedom has a mean of 0 and a standard deviation of sqrt(10 / (10 - 2)) = sqrt(10 / 8) = sqrt(5 / 4). So, the probability of getting a t-statistic of 2 or higher is 0.05.

What is the probability of getting an F-statistic of 4 or higher from an F-distribution with 5 and 10 degrees of freedom?

  1. 0.05

  2. 0.10

  3. 0.15

  4. 0.20


Correct Option: A
Explanation:

The F-distribution with 5 and 10 degrees of freedom has a mean of 5 and a standard deviation of sqrt(2 * 5 * 10 / (5 - 2)) = sqrt(100 / 3) = sqrt(100 / 3). So, the probability of getting an F-statistic of 4 or higher is 0.05.

What is the probability of getting a correlation coefficient of 0.5 or higher from a population with a correlation coefficient of 0.5?

  1. 0.05

  2. 0.10

  3. 0.15

  4. 0.20


Correct Option: B
Explanation:

The sampling distribution of the correlation coefficient is a t-distribution with n-2 degrees of freedom, where n is the sample size. In this case, the sampling distribution of the correlation coefficient has 100-2 = 98 degrees of freedom. The probability of getting a correlation coefficient of 0.5 or higher is 0.10.

What is the probability of getting a regression coefficient of 2 or higher from a population with a regression coefficient of 2?

  1. 0.05

  2. 0.10

  3. 0.15

  4. 0.20


Correct Option: A
Explanation:

The sampling distribution of the regression coefficient is a t-distribution with n-2 degrees of freedom, where n is the sample size. In this case, the sampling distribution of the regression coefficient has 100-2 = 98 degrees of freedom. The probability of getting a regression coefficient of 2 or higher is 0.05.

What is the probability of getting an ANOVA F-statistic of 4 or higher from a population with an ANOVA F-statistic of 4?

  1. 0.05

  2. 0.10

  3. 0.15

  4. 0.20


Correct Option: A
Explanation:

The sampling distribution of the ANOVA F-statistic is an F-distribution with k-1 and n-k degrees of freedom, where k is the number of groups and n is the total sample size. In this case, the sampling distribution of the ANOVA F-statistic has 2-1 = 1 and 100-2 = 98 degrees of freedom. The probability of getting an ANOVA F-statistic of 4 or higher is 0.05.

What is the probability of getting a chi-square goodness-of-fit statistic of 10 or higher from a population with a chi-square goodness-of-fit statistic of 10?

  1. 0.05

  2. 0.10

  3. 0.15

  4. 0.20


Correct Option: A
Explanation:

The sampling distribution of the chi-square goodness-of-fit statistic is a chi-square distribution with k-1 degrees of freedom, where k is the number of categories. In this case, the sampling distribution of the chi-square goodness-of-fit statistic has 5-1 = 4 degrees of freedom. The probability of getting a chi-square goodness-of-fit statistic of 10 or higher is 0.05.

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