Statistics and Probability Assignment Solution for Data Analysis

This assignment solution covers several key concepts in statistics and probability. It includes the calculation of marginal and conditional probabilities, demonstrating an understanding of probability distributions and their applications. The solution also involves a chi-square statistical test, analyzing a contingency table to determine the relationship between categorical variables, and calculating the degrees of freedom and probability associated with the test. Furthermore, the assignment addresses descriptive statistics, specifically calculating the mean, mode, and median of a dataset, and interpreting these measures to convey specific information about the data's distribution. The solution provides a detailed breakdown of each step, showing the methodology and rationale for each calculation.

1. Marginal probability of no rain: 0.05+0.1+0.1+0.05=0.3
2. Marginal probability of heavy rain: 0.1+0.2+0.05+0.01=0.36
3. Conditional probability that there is Heavy Rain given there is Some Wind (Pr(Rain =Heavy
Rain | Wind = Some Wind)) = 0.2
4. let P(x) be probability of hiring x number of women
then probability of hiring 3 or fewer women = P(0)+P(1)+P(2)+P(3)
now P(0) = (0.6)12 =0.00217
P(1) = (0.4)(0.6)11 = 0.00145
P(2) = (0.4)2(0.6)10 = 0.00096
P(3) = (0.4)3(0.6)9 = 0.00064
therefore P(x<=3) = P(0)+P(1)+P(2)+P(3) = 0.00524
5. The results of a contingency table X2 statistical test performed
data: contingency table
A B C D
1 30 12 33 29 104
2 19 18 15 32 84
3 12 26 8 19 65
61 56 56 80 253
expected: contingency table

A B C D
1 25.1 23.0 23.0 32.9
2 20.3 18.6 18.6 26.6
3 15.7 14.4 14.4 20.6
chi-square = 26.1
degrees of freedom = 6
probability = 0.000
6.
Mean 42.28
Mode 65
Median 35
The division should send the Median age as it is 35 and the mean is 42.28. To show the division
younger, median is suitable.