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Probability that the download time is above 1.8 seconds for Business Name Course Number Date Faculty Name Mathematics for Business PART A

   

Added on  2021-05-31

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Statistics and Probability
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Mathematics for BusinessNameCourse NumberDateFaculty Name
Probability that the download time is above 1.8 seconds for Business Name Course Number Date Faculty Name Mathematics for Business PART A_1

Mathematics for BusinessPART AThe average download time is 2 seconds and a standard deviation of 0.5 seconds. a)The probability that the download is above 1.8 seconds?z−score=x−meanstandarddeviation1.8−20.5=−0.4The probability associated with the z-score value of -0.4 is less than 0.001. Therefore, theprobability of the download time being above 1.8 seconds is above 0.999. b)The probability that the download is between 1.5 and 2.5Z−scores=1.5−20.5<Z<2.5−20.5−1<Z<1probabilityofZ←1=0.1587ProbabilityofZ<1=0.8413The probability of the download time is between 1.5 and 2.5 seconds is 0.8413−0.1587=0.6826
Probability that the download time is above 1.8 seconds for Business Name Course Number Date Faculty Name Mathematics for Business PART A_2

c)99% of the download times are slower than how many seconds?Zscoreat99%=−2.33−2.33=X−20.5(0.5∗−2.33)+2=XX=2−1.1650.835secondsPART B
Probability that the download time is above 1.8 seconds for Business Name Course Number Date Faculty Name Mathematics for Business PART A_3

IntroductionNormal distribution is among the most used distributions in statistics. Their distributioncan be in different formats based on the mean and standard deviation. These statistics determinethe position and the shape. A widely distributed population has a normal distribution which has alarge kurtosis and longer tails. In addition, a population whose values are not approximatelydistributed around the mean has a skewness statistic which is not equivalent to zero1. A negativeand positive skew indicates that the left and right tail are longer respectively – hence the meanand median statistics are not equal. Therefore, using lower and higher moments of statistics, thedistribution of data can be effectively described. In a normally distributed population, respectiveprobability values can be estimated using the standard normal and inverse standard normaltables2. There are various theoretical assumptions which can be used in determining whether asample is skewed or approximately normal. Also, boxplots, histograms and QQ-plots can be usedto check normality. In this paper, we will use the standard normal table, boxplot, histogram andQQ-plot to check for normality of utility charges (electricity costs) of one-bedroom units in acertain city. Results & Discussionsa)Constructing BoxplotTable 1: Summary statistics of Utility charges (Electricity costs)Utility Charge (Electricity Costs)Mean147.06Standard Error4.482Median148.5Mode130Standard Deviation31.691Sample Variance1004.343Kurtosis-0.5441Abdal-sahib et al., “Testing for Normality.”2Fletcher, “Normal Distribution.”
Probability that the download time is above 1.8 seconds for Business Name Course Number Date Faculty Name Mathematics for Business PART A_4

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