BUS130 Statistics Assignment MAIS

BUS130 Statistics Assignment PART A: Consumers spend an average of $21 per week in cash without being aware of where it goes (data extracted from ‘Snapshots: A Hole in Our Pockets,’ USA Today, January 18, 2010, p. 1A). Assume that the amount of cash spent without being aware of where it goes is normally distributed and that the standard deviation is $5. (a) What is the probability that a randomly selected person will spend more than $25? (b) What is the probability that a randomly selected person will spend between $10 and $20? (c) Between what two values will the middle 95% of the amounts of cash spent fall? (Formula used for a and b) a) z = (25-21)/5 = + 0.8 The area under the standard normal curve right to the z value indicates the required probability. P(X>25) = P (z > 0.8) = 0.2119 b) z1 = (10-21)/5 = - 2.2 z2 = (20-21)/5 = - 0.2 The area under the standard normal curve between these two z values indicates the required probability. P(10 < X < 20) = P(- 2.2 < z < 0- 0.2) = 0.4861 (z1) - 0.0793 (z2) = 0.4068 c) The middle 95% is represented as 0.9500, which suggests that 0.9500/2 = 0.4750 will fall at both left and right of the mean. The z value corresponding to 0.4750 area is 1.96. Therefore, Required X values are Mean +/- (z*SD) Mean +/- (1.96*5) = 9.8 21 - 9.8 = 11.2 21 + 9.8 = 30.8 The Middle 95% of the amounts of cash spent fall between $11.20 and $30.80. PART B: The file Property Taxes contains the property taxes per capita for the 50 states and the District of Columbia. Decide whether the data appear to be approximately normally distributed. Decide whether the data appear to be approximately normally distributed by: (a) Constructing a box plot. (b) Constructing a histogram. (c) Comparing data characteristics to theoretical properties. (d) Constructing a Quantile-Quantile Normal Probability Plot. Introduction: Statistics can be defined as the set of methodologies for collecting, representing, analysing and interpreting data (Goos and Meintrup 2015). Statistics is often used to collate data and create a visual representation of this data