The average weekly earnings of bus drivers in a city are $950 (that is μ) with a standard deviation of $45 (that is σ). Assume that we select a random sample of 81 bus drivers. What is the probability that the sample mean will be greater than $960? (Keep 4 digits of the result)
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- The Baker Company wants to develop a budget to predict how overhead costs vary with activity levels. Management is trying to decide whether direct labor hours (DLH) or units produced is the better measure of activity for the firm. Monthly data for the preceding 24 months appear in the file P13_40.xlsx. Use regression analysis to determine which measure, DLH or Units (or both), should be used for the budget. How would the regression equation be used to obtain the budget for the firms overhead costs?Use Excels functions (not @RISK) to generate 1000 random numbers from a normal distribution with mean 100 and standard deviation 10. Then freeze these random numbers. a. Calculate the mean and standard deviation of these random numbers. Are they approximately what you would expect? b. What fraction of these random numbers are within k standard deviations of the mean? Answer for k = 1; for k = 2; for k = 3. Are the answers close to what they should be (about 68% for k = 1, about 95% for k = 2, and over 99% for k = 3)? c. Create a histogram of the random numbers using about 10 bins of your choice. Does this histogram have approximately the shape you would expect?4.1 TYPES OF RANDOM VARIABLES. Which of the following describe continuous random variables? Which describe discrete random variables? The number of newspapers sold by the New York Times each month The amount of ink used in printing a Sunday edition of the New York Times The actual number of ounces in a 1-gallon bottle of laundry detergent The number of defective parts in a shipment of nuts and bolts The number of people collecting unemployment insurance each month
- Discuss in 300 words the different types of probability sampling designs and briefly explain how these differ from non-probability sampling approaches. Provide at least two relevant references.1.The reported unemployment is 5.5% of the population. What measurement scale is used to measure unemployment? Interval Nominal Ordinal Ratio 2.Which one of the following is NOT an example of discrete data? Number of employees reporting in sick Number of households watching the Home Shopping Network Number of miles between New York City and Chicago Number of members of the Denver Lions Club4. ABC Dog Food Company located in Ottawa sells large bags of dog food to warehouse clubs. ABC uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 50 kilograms and a standard deviation of 1.25 kilograms. (a) What is the probability that a filled bag will weigh less than 49.5 kilograms? (b) What is the probability that a randomly sampled filled bag will weigh between 48.5 and 51 kilograms? (c) What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled? (d) ABC is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that 2% of all filled bags weigh more than 52 kilograms?
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- Bo Using data from 50 workers, a researcher estimates Wage = ẞe + B₁Education + B2Experience + B3Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A portion of the regression results is shown in the following table. Intercept Education Experience Age Coefficients Standard Error t Stat p-Value 7.17 4.26 1.68 0.0991 1.81 0.35 5.17 0.0000 0.45 0.10 4.50 0.0000 -0.01 0.06 -0.17 0.8684 a-1. Interpret the point estimate for ẞ1. As Education increases by 1 year, Wage is predicted to increase by 1.81/hour. As Education increases by 1 year, Wage is predicted to increase by 0.45/hour. As Education increases by 1 year, Wage is predicted to increase by 1.81/hour, holding Age and Experience constant. As Education increases by 1 year, Wage is predicted to increase by 0.45/hour, holding Age and Experience constant. a-2. Interpret the point estimate for $2. As Experience…Bill Hardgrave, production foreman for the Virginia Fruit Company, estimates that the average sales of oranges is 4,700 and the standard deviation is 500 oranges. Sales follow a normal distribution.a) What is the probability that sales will be greater than 5,500 oranges?b) What is the probability that sales will be greater than 4,500 oranges?c) What is the probability that sales will be less than 4,900 oranges?d) What is the probability that sales will be less than 4,300 oranges?From several years’ records, a fish market manager has determined that the weight of deep sea bream sold in the market (X), is approximately normally distributed with a mean of 500 grams and a standard deviation of 100 grams. Assuming this distribution will remain unchanged in the future, the expected proportions of deep sea bream sold over the next year weighing .(i) Between 300 grams and 400 grams is A. 0.1359 B. 0.4681 C. 0.5319 D. None of the options above