Given the following frequency distribution for n = 100. Class intervals Frequency 0-under 10 20 a. Approximate the mean. 10-under 20 10 b. Approximate the standard deviation. 20-under 30 20 30-under 40 30 40-under 50 20 100 a. X= (Type an integer or a decimal.) b. S= (Round to two decimal places as needed.)b. Is there a relationship between the variables? Is it positive or negative? O There is no relationship between the two variables. O The relationship is positive because owner mileage is almost exactly equal to government mileage. O The relationship is positive because as one variable increases, the other variable also tends to increase. O The relationship is negative because owner mileage is usually below the government mileage.Let's look at an application of statistics in your daily life. To classify a new email message in your inbox as either spam or a legitimate message, we would first need to add to your email program a 'spam filter that has the ability to track word frequencies associated with spam and legitimate messages as you identify them on a day-to-day basis. Assume that the word 'offer' occurs in 75% of the spam messages in your inbox. Also, let's assume 'offer' occurs in 15% of my legitimate emails. If 25% of the received emails are considered as a spam, and I will receive a new message which contains the word "offer', what is the probability that it is a spam? O A. 0.625 O B. 0.675 O C. 0.655 O D. 0.774A sample of 500 respondents was selected in a large metropolitan area to Gender study consumer behavior. The resulting contingency table is shown to the right. Enjoys shopping for clothing Male Female Total Complete parts (a) through (c). Yes 128 237 365 No 102 33 135 Total 230 270 500 a. Suppose the respondent chosen is a female. What is the probability that she does not enjoy shopping for clothing? P(does not enjoy shopping female) = (Round to four decimal places as needed.) b. Suppose the respondent chosen enjoys shopping for clothing. What is the probability that the individual is a male? P(male|enjoys shopping) = (Round to four decimal places as needed.) c. Are enjoying shopping for clothing and the gender of the individual statistically independent? Explain. O A. No, because P(male|enjoys shopping) # P(male). O B. No, because P(male|enjoys shopping) = P(male). O C. Yes, because P(male|enjoys shopping) # P(male). O D. Yes, because P(male|enjoys shopping) = P(male).The following table compares fuel economy as calculated by car owners and by 21. Choose he correct graph below. government standards. Car Owner (x) Government (v) I: A 14.1 16.1 B 3?.8 42.6 C 25.5 23.6 D 23.4 28.4 E 1T.'l 1?.3 F 3?.1 42.0 G 28.6 36.1 H 28.9 30.0 | 33.6 48.9 :1. Construct a scatter diagram to investigate the relationship between owner calculated mileage and government calculated mileage. b. Is there a relationship between the van'ables'? Is it positive or negative? b. Is there a relationship between the van'ables? Is it positive or negative