Question 18 A province-wide survey was conducted on a group of adult women in regards to their marital status. The following table shows the marital status of the adult women surveyed, broken down by age group. A woman was picked randomly from the group. M Status Age 18-29 30-64 65+ Total Married 7.500 42,100 8.250 57,850 Never married 13,150 7,200 800 21,150 Widowed 30 3.250 8,150 11,430 Divorced 730 9,300 1,150 11,180 Total 21,410 61,850 18,350 101,610 Find the probabilities of the following events. Round to 3 decimal places of accuracy: a. What is the probability that the woman chosen is I ween the ages 18 to 29? Number b. What is the probability that the woman chosen is between ages 18 to 29 and has never married? Number EDto c. What is the probability that the woman chosen is divorced, given the information that she is in the 30 to 64 age group? Number d. What is the probability that the woman chosen is either widowed or 65+? Number c. What is the probability that the woman chosen is neither widowed nor 65+? Number f. What is the probability that the woman chosen is not in the age group 30 to 64? Number g. Are the two events that the woman is Married and that the woman is in the age group 30 to 64 mutually exclusive? O No Yes h. Are the two events that the woman is Married and that the woman is Divorced mutually exclusive? O No Yesf. What is the probability that the woman chosen is not in the age group 30 to 64? Q Number + g. Are the two events that the woman is Married and that the woman is in the age group 30 to 64 mutually exclusive? No Yes h. Are the two events that the woman is Married and that the woman is Divorced mutually exclusive? O No Yes i. Are the two events that the woman is Married and that the woman is Divorced complementary events? O No Yes j. Are the two events that the woman is Married and hat the woman in the age group 30 to 64 independent? Yes O NoA Quesoon 79 A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music, Let a be the number of puzzles completed successfully by a subject, The psychologist found that a had the following probability distribution: O P (x) 0.3 2 3 4 0.25 0.2 0.25 a. Find the mean (/) of the discrete random variable c. (Note: Round to 2 decimal places of accuracy) Number b. Find the standard deviation (o) of z. (Note: Round to 2 decimal places of accuracy) Number c. Find the probability that a randomly chosen subje completes at least 1 puzzle(s) in the five-minute period while listening to soothing music. (Note: Round to 2 decimal places of accuracy) NumberQuestion 20 Household Size in Senegal According to CEOWORLD magazine, Senegal had the largest household size in the world in 2020. A researcher randomly $ points selected n = 25 Senegalese households and found the following data: Household Size (Senegal) Household size Number of households (I) 0 -2 2 - 4 2 4 - 6 3 5 - 8 4 8 - 10 6 10 - 12 9 Using the sample formulas, answer the following questions. Round to two decimals if necessary. a. Find the average household size. Number b. Find the sample variance.Number b. Find the sample variance, Number c. Find the sample standard deviation. Number d. Based on this frequency distribution, the distribution of the household size is normal (not skewed). skewed to right. skewed to left. e. Which of the following is the median class (the class interval where the median household size lies)? O 10-12 0 6 -8 O 8 - 10