Question 1 (a)Frequency distribution (b)Histogram (c)Calculation of mean, median and mode : Sorted data 1
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MeanTotal data points n = 60 Sum of data points = 62600 Mean = Sum of data points / Total data points MedianN= even number Formula to find the Median ModeHighest frequency observed for data point 401. Mode = 401 Question 2 (a)The data provided would be regarded as a sample. The main reason behid the above conclusion is that the data of sales is only offered for selective seven weeks and it does not include round the year data. Since, selective data which is part of the population data is represented then, it is called a sample. (b)Computation of standard deviation for the variable weekly attendance 3
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Total sample data points n = 7 Sum of data points = 3392 Mean of the sample = Sum of data points / Total data points The table to calculate the standard deviation is shown below: Formula to find the standard deviation for sample is shown below: 4
Therefore,standard deviation for sample is 74.06. (c)Calculation of inter quartile range First quartile and third quartile needs to be calculated in order to find the inter quartile range. Sorted data set οCalculation of First quartile (Q1) or 25thpercentile οCalculation of third quartile (Q3) or 75thpercentile (d)r (correlation coefficient) Variables 5
Independent variable: weekly attendance Dependent variable: Number of chocolate bars sold Formula to find thecorrelation coefficient of the variables is shown below: Question 3 Estimation of regression equation 6
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The value of a and b is a function of x and y which is shown below: Regression equation Example: Case 1: weekly attendance = 0.00 Case 2: The increase in studentsβ quantity by 10 would lead to an increase in the sales of bars by 1068 units. This has been derived = 10*10.677 where 10.677 is the slope coefficient of the regression equation above. 7
(b) R square (coefficient of determination) Question 4 The given information is represented below: (a)P (Player from Holmes OR taking Grassroots training) (b)P (Player external AND taking scientific training) 8
(c)P (Player from Holmes AND taking scientific training) (d)Let X event: Training Y event: Recruitment X and Y would be independent when, P (X) * P (Y) = P (X AND Y) Here, P (X) * P (Y) = 0.1573 Further, P(X AND Y) = 0.2576 Condition is not satisfied and therefore, event X and Y i.e. training and recruitment are dependent events. Question 5 9
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= 0.32 Bayesian Probability formula would be used in regards to find the probability that customer will select segment A and product X. There is 35.37% probability that customer will select segment A and product X. (b) The probability that customer will select product X. = 0.32 There is 32% probability that customer will select product X. Question 6 (a)Binomial Distribution 10
P (x less than equal to 2) = Total trials = 8 Probability of total success = 0.1 P (x less than equal to 2) = 0.9619 96.19% is the probability that 2 or less than 2 customers would make a purchase from the shop. (b)Poisson distribution Where, Now, 12.4% is the probability that in 2 minutes there would be 9 customer who will come to shop. 11
Question 7 (a)Probability (x higher than $2 million) =? Normal distribution Where, (b)Probability ( between $1.1 million and $1 million) =? Normal distribution Where, 12
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Question 8 (a)The key question is whether z can be sued as test statistic or not. This would essentially depend on the sample sie since when the sample size is large, an assumption can be made that the distribution is normal. In this regards, the minimum sample size is considered to be 30 as envisaged by the Central Limit Theorem. This condition is fulfilled here and hence the use of z for analysis is permissible. (b)Total investors = 45 Investors agree to invest = 11 Now, 13