Measure of dispersion | Mathematics homework help

QUESTION 1 (20) State whether each of the statements below is TRUE or FALSE. If FALSE, provide a reason. 1.1. In a data set, the range is a measure of dispersion. 1.2. The most frequently occurring value in a data set is called the median. 1.3. The most passive data collection method is experimentation. 1.4. In linear correlation, a Pearson’s correlation coefficient of indicates a weak and indirect relationship between the variables. 1.5. The outcome of an examination is an example of a binomial experiment. 1.6. Approximately 95% of the area below the normal distribution curve lies between and . 1.7. The volume of water consumed by an athlete during the Comrades Marathon is quantitative and discrete. 1.8. There are three quartiles in a data set. QUESTION 2 (20) The following data give the hourly wage rates (Rands) for a sample of 20 workers selected from a large company. 12.50 9.45 13.85 7.25 8.70 14.60 11.75 14.50 10.80 12.45 7.50 15.90 9.75 11.50 13.30 6.25 15.50 12.80 5.35 9.50 2.1. Using the raw data, determine the range. (2) 2.2 Group the data into a frequency distribution with a lowest class lower limit of R 5.00 and a class width of R 2.00. (7) 2.3 Determine the mean wage rate using the raw data. (3) 2.4 Draw an OGIVE curve corresponding to the data and use it to estimate the median. (8) QUESTION 3 (20) The following data represents the number of cellular phones sold by an agent for 50 consecutive days. Cellular phones sold Frequency 1 – 13 7 14 – 26 6 27 – 39 5 40 – 52 9 53 – 65 15 66 – 78 8 3.1 For the 50-day period, calculate the: 3.1.1 mean number of cellular phones sold. (9) 3.1.2 modal number of cellular phones sold. (2) 3.2 Determine the standard deviation QUESTION 4 (20) 4.1 The Food and Drug Administration (FDA) approves 20% of drugs submitted for its approval. Find the probability that in a sample of 15 drugs submitted for the FDA’s approval, the number of drugs that are approved is: 4.1.1 exactly 4 (4) 4.1.2 at most 2 (8) 4.2 State two properties of the normal distribution function. (2) 4.3 A racing car is one of the many toys manufactured by Mack Corporation. The assembly time for this toy follows a normal distribution with a mean of 55 minutes and a standard deviation of 4 minutes. The company closes at 5pm every day. If one worker starts assembling a racing car at 4pm, what is the probability that she will finish this job before the company closes for the day? (6)

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