Part 1 Of 9, Question 1 Of 2510 Points Sample Of 20 Observat ✓ Solved
Part 1 Of 9 Question 1 Of 2510 Pointsa Sample Of 20 Observations Has
Part 1 of 9 - Question 1 of .0 Points A sample of 20 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is: A.400 B.320 C.304 D.288
Part 2 of 9 - Question 2 of .0 Points What type of probability uses sample spaces to determine the numerical probability that an event will occur? A.classical probability B.conditional probability C.empirical probability D.subjective probability
Question 3 of .0 Points If A and B are any two events with P(A) = .8 and P(B|A) = .4, then the joint probability of A and B is A.0.32 B.0.80 C.0.40 D.1.20
Part 3 of 9 - Question 4 of .0 Points Find the variance of the following probability distribution. X P(X) .....10 A.1.83 B.1.31 C.1.25 D.1.71
Question 5 of .0 Points Which term is NOT synonymous with the expected value of a discrete probability distribution? A.variance B.mean C.theoretical average D.μ
Part 4 of 9 - Question 6 of .0 Points If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct. Each question has four possible choices. A.0.19 B.0.17 C.0.08 D.0.23
Question 7 of .0 Points The continuous distribution characterized by a symmetric, bell-shaped curve is the: A.binomial distribution B.Poisson distribution C.exponential distribution D.normal distribution
Part 5 of 9 - Question 8 of .0 Points The standard deviation of a probability distribution must be: A.a nonnegative number B.a negative number C.a number between 0 and 1 D.less than the value of the mean
Question 9 of .0 Points The mean of a probability distribution can be: A.a positive number B.a negative number C.zero D.all of the above
Part 6 of 9 - Question 10 of .0 Points The standard deviation of the sampling distribution of the mean is usually called the: A.standard error of the population B.randomized standard error C.standard error of the mean D.standard error of the sample
Question 11 of .0 Points The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the: A.point estimate theorem B.central limit theorem C.simple random sample theorem D.central tendency theorem
Part 7 of 9 - Question 12 of .0 Points The standard normal distribution has a mean of ___ and standard deviation of ___, respectively. A.1 and 1 B.0 and 0 C.1 and 0 D.0 and 1
Part 8 of 9 - Question 13 of .0 Points Accepted characters : numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A statistics professor has just given a final examination in his statistical inference course. He is particularly interested in learning how his class of 40 students performed on this exam. The scores are shown below. What is the median score on this exam? Place your answer, rounded to two decimal places in the blank. For example, 65.78 would be a legitimate entry. ___________
Part 9 of 9 - Question 14 of .0 Points Accepted characters : numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. In a survey, 55% of the voters support a particular referendum. If 40 voters are chosen at random, and X is the number of voters that support this referendum, find the mean and variance of X. Place the mean in the first blank _______and place the variance in the second blank. -_______________ Question 15 of .0 Points Accepted characters : numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A DVD rental business determines that customers will rent X number of DVDs according to the following distribution: Number of DVDs rented X Probability P(X) 0.....05 What is the mean number of DVDs that customers rent? Round your answer to one decimal place as necessary. For example, 4.5 would be a legitimate entry. Answer: ____________ Part 10 of 9 - Question 16 of .0 Points Accepted characters : numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A certain system has two components. There are 10 different models of the first component and 10 different of the second. Any first component can be paired with any second component. A salesman must select 2 of the first component and 3 of the second to take on a sales call. How many different systems can the salesman select? Place your answer in the blank. DO NOT use commas. For example, 2350 would be a legitimate response. _____________ Question 17 of .0 Points Accepted characters : numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. Mothers Against Drunk Driving (MADD) is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below: Number of Vehicles Involved Did alcohol play a role? Yes No What proportion of accidents involved alcohol and a single vehicle? Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry. ____________ Part 8 of 9 - Question 18 of .0 Points Accepted characters : numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A Wendy’s fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30. How many chicken sandwiches must the restaurant stock to be 99% sure of not running out on a given day? Place your answer, rounded to the nearest whole number in the blank. For example, 345 would be a legitimate entry. ___________ Question 19 of .0 Points Accepted characters : numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. The average hourly wage of workers at a fast food restaurant is $6.50/hr with a standard deviation of $0.45. Assume that the distribution is normally distributed. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1776 would be a legitimate entry. ____________ Question 20 of .0 Points Accepted characters : numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random. Find the mean of the sampling distribution of the means of average weekly earnings for samples of size 100. Place your answer in the blank. Do not include a dollar sign. For example, 123 would be a legitimate entry. _____________ Question 21 of .0 Points Accepted characters : numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9. What is the probability that a randomly selected customer will spend $20 or more at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry. ___________ Question 22 of .0 Points Accepted characters : numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8. What is the probability of getting a score of 91 or less on this exam? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry. _________ Question 23 of .0 Points Accepted characters : numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. Mrs. Smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. Assuming that the distribution of words read per minute are normally distributed, what is the minimum number of words per minute a student would have to read in order to get the award? Place your answer, rounded to the nearest whole number , in the blank. _________ When entering your answer do not use any labels or symbols. Simply provide the numerical value. For example, 123 would be a legitimate entry. Part 9 of 9 - Question 24 of .0 Points The left half under the normal curve is slightly smaller than the right half. True False
Sample Paper For Above instruction
The question prompts cover a wide range of topics in statistics, including basic descriptive statistics, probability distributions, statistical inference, and applications of normal distribution. For this paper, we will explore these concepts in detail, illustrating their importance and applications in real-world statistical analysis, with references to scholarly sources and practical examples.
Introduction
Statistics is a discipline that allows researchers and analysts to interpret data, make predictions, and infer characteristics of populations based on sample data. Fundamental to statistics are concepts such as measures of central tendency, variability, probability distributions, and inferential methods. The initial questions relate to basic descriptive statistics, such as the sum of squared deviations, and probability calculations based on sampling distributions. Understanding these foundations is essential for advanced analysis and decision-making processes.
Sum of Squared Deviations
In the first question, a sample of 20 observations with a standard deviation of 4 is provided. The sum of squared deviations from the sample mean is a critical component in variance calculations. Variance (s²) is defined as the average of squared deviations from the mean and is expressed as:
Variance = (Sum of squared deviations) / (n - 1)Given the sample standard deviation (s) is 4, the variance is:
4² = 16Multiplying variance by (n - 1), we find the total sum of squared deviations:
Sum of squared deviations = Variance x (n - 1) = 16 x 19 = 304This matches option C (304). Such calculations underscore the importance of understanding variance and the sum of deviations in summarizing variability within data sets.
Types of Probability
The second question addresses different types of probability: classical, conditional, empirical, and subjective. Classical probability uses sample spaces and equally likely outcomes to determine probabilities, making it fundamental in classical probability theory used in games of chance and lotteries (Ross, 2014). Empirical probability, on the other hand, is based on observed data rather than theoretical models. Conditional probability involves the likelihood of an event A given that event B has occurred. Recognizing these types is vital in designing experiments and interpreting statistical results correctly.
Joint Probability and Conditional Probability
The third question involves computing joint probability using the formula:
P(A ∩ B) = P(A) × P(B|A)Given P(A) = 0.8 and P(B|A) = 0.4, the joint probability is:
0.8 × 0.4 = 0.32This calculation confirms the understanding of how conditional probabilities relate to joint and marginal probabilities, and is fundamental in Bayesian inference and risk assessment.
Variance of a Probability Distribution
The fourth question involves calculating the variance for a given probability distribution. Variance quantifies the spread of a distribution and is calculated as:
Variance = Σ [ (x - μ)² * P(x) ]Where μ is the mean, and the sum extends over all possible values of x. Accurate computation of variance is essential for understanding data variability, risk measurement, and statistical modeling (Casella