Probability Analysis - Assignment Example

1. It’s a single value histogram that means that it does not involve intervals. A histogram bar of 20 represents people aged 20, not from 20 to 30. Therefore the percentage of individuals below the age of 35 will be the individuals below 40 (since it’s a single value histogram): Number of people below 35 = 3+18+13= 34 Percentage of people below 35 = (34/50)*100= 68% 2. The histogram is skewed to the right. This is because its right tail is longer than its left tail. This is also due to the reason that the tail on the right is more positive than the tail on the left. Furthermore this is also due to the fact that values with higher frequency lie to the left making the histogram right skewed. 3. Mean = (10*3 + 20*18 + 30*13 + 40*6 + 50*5 + 60*3 + 70*1 + 80*0 + 90*1)/50 = 1610/50 = 32.2 4. The media calculation is as follows: 50/2 = 25th value = age 30 5. The mean will increase since the mean is affected by extreme values of a data set. Calculation shows it: New mean = (10*3 + 20*18 + 30*13 + 40*6 + 50*5 + 60*3 + 70*1 + 80*0 + 900*1)/50 = 2420/50 = 48.4 However the median will stand unaffected, since the media is the middle value of the data set, it is based on the number of recorded observations not on the value of recorded observation. There for the since the number of observation under each condition is 50 the median is as follows: 50/2 = 25th value = age 30 6. The events A and B are mutually exclusive since the chances of heads coming on the first toss is not related to or has an impact on the chances of heads coming on the fifth toss, therefore the two events stand mutually exclusive. 7. The events A and B are independent since the heads occurring on the first toss doesn’t have an impact on the probability of heads occurring on the fifth toss. 8. Mean = (110+95+131+257+118+153)/6 = 144 X X-Mean (X-Mean)^2 110 -34 1156 95 -49 2401 131 -13 169 257 113 12769 118 -26 676 153 9 81 Standard Deviation = [(∑ (x-Mean)^2)/n-1)]^1/2 = (17252/49)^1/2 = 18.76 9. One of the movie length of 257 appears to be unusual, it is significantly different form all the other values. It appears more like an outlier in the data set. 10. Big Burg has greater variability since its values are more dispersed than that of tiny town. The values of tiny town range from approximately 30 to 130 while that of Big Burg range from 20 to beyond 140. 11. Big Burg. This is because it has greater magnitude of values beyond $85000 and over. 12. Big Burg. This is because the width of the Box Plot shows that Big Burg shows that there are more real estate values from $ 55000 to $85000. 13. 99% confidence interval: Mean ± Z (standard deviation/(n)^1/2) Mean = 182.5 pounds SD = 22.5 pounds Z value = 2.565 Lower CI = 172.45 pounds Upper CI = 192.54 pounds 14. Students in French class only = 12 Students in Spanish class only = 15 Probability of student being picked form single class = (12+15)/500 = 0.054 15. Student in Spanish class also in French class = 17/500 = 0.034 16. No. of elements in the sample space = 10 17. Probability that all elements are not all the same = 3((1/10)*(1/10)*(9/10)) = 0.027 18. Probability that all three numbers drawn are different = 3 ( ( 1/10)*(9/10)*(8/10)) = 0.216 19. Expected Value of X = (-3*0.08)+(-2*0.11)+ ( 4*0.28) + (6*0.12) +(7*0.41) = 4.25 20. Standard Deviation = [(∑(x-mean)^2(P(x))/N]^1/2 = [11.9875/5]^1/2 = 1.548 21. Probability of having enough seats = 10/12 = 0.8333 22. Passengers expected to show up = 0.80*12 = 9.6 since passengers are not in decimal this will be rounded up to 10 passengers. 23. It is a left tailed test. Z-value from table for significance level of 10% = -1.275 Z-value calculated = (Sample mean- Population mean)/(sample standard deviation/n^1/2) = (726.2-750)/(85.3/(22^1/2)) = -1.308 Since the z- value calculated lies in the rejection region i.e. its smaller than -1.275 therefore we reject Ho. This means that the population mean is not 750. 24. Probability tire lasts longer than 38100 miles= 1-(probability(x≤38100)) = 1-probability ((38100-30000)/5000) = 1- 0.9474 = 0.0526 25. Numbers of tires within 33800 and 27500 miles. P(27500 Read More