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Numerade Educator



Problem 109 Hard Difficulty

gives the number of suicides estimated in the U.S. for a recent year by age, race (black or white), and sex. We are interested in possible relationships between age, race, and sex. We will let suicide victims be our population.
Do not include "all others" for parts f and g.
a. Fill in the column for the suicides for individuals over age 64.
b. Fill in the row for all other races.
c. Find the probability that a randomly selected individual was a white male.
d. Find the probability that a randomly selected individual was a black female.
e. Find the probability that a randomly selected individual was black
f. Find the probability that a randomly selected individual was male.
g. Out of the individuals over age 64, find the probability that a randomly selected individual was a black or white male.


a) $\left(\begin{array}{l}{4870+890} \\ {+140+20+100}\end{array}\right)=6020$
b) $\left(\begin{array}{l}{4870+890} \\ {+140+20+100}\end{array}\right)=6020$
c) 0.74
d) 0.011
e) 0.067
f) 0.797
g) 0.83


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Video Transcript

Yeah, Hi. We're looking at question 109 and there are several parts to this question, so we'll just work our way through them, starting with part A where they want us to fill in the column that says, um, workout, getting suicides for individuals over 64. So they've gathered information on suicides from different ages, races and sexes and compile them into a table. But the table is incomplete. So since we're filling in a column, we're going to use our row information to calculate each of these. So starting with the white male row to be able to fill in the column over 64 we start with the total, which is 22,050 and then we're going to subtract. Each of the values that we know so well do is attract to 10 for the one through 14 age bracket, 3360 for the 15 through 24 age bracket, and 13,610 for the 25 3 64 bracket, which leaves 4870 for the over 64. We're gonna follow a similar pattern for the white female, the total for the row is 4930 and we will subtract 80 for the first column, 580 for the second and then 3380 for the third, leaving us with a total for the over 64 of 890. Now we'll do the same thing with the blackmail. The total is 1670. Then we'll subtract the 10 from the first column, the 4 60 from the second column and that 1060 from the third column, which leaves us with 140 for that room. And then we'll do the black female rose, similarly, 330 and subtract the zero for the first column, the 40 for the second column and the 2 70 for the third column, leaving us with 20 for the over 64 set. And then I'm changing to Red because we're going to jump to totals because they all others row is empty. We can't fill that one in on its own, but we can fill in our total and then use all of our information to go back and get the aloe others spot. So our total we have 29,760 and then we can subtract each of the values from that row. So that would be 3 10 and subtract 4650 for the second column in 18,780 for the third column, which leaves us with 6020. Now we can use that 6020 here and subtract are answers that we got right here. So we'll subtract the 4870 subtracted 8 90 Subtract the 1 40 subtract the 20. So you want to be careful that you've done your subtractions. They're carefully to make sure that you get the right answers so that this one's correct. And so we have 100 for the all others. So we've now successfully filled in the overt 64 column for part A for part B. We're going to work similarly through the all others row now. So now we're cause we're working the road. We're gonna use the columns to do the subtraction. So for the one through 14 set, we have a total of wow how that happened. Um a total. I mean, erase those for you and we'll go back and try this again. So we have a total of 310 and we're going to subtract the 210 and subtract the 80. So I'm just going down the column in this case and then subtract the 10 and subtract the zero. So that leaves for the all others. I'm 10. Similarly, I'm gonna take the total for the column 15 to 24 which is 4650. And I'll subtract the white male, which is 3360 and subtract the white female, which is 5 80 and then subtract the blackmail, which is for 60 and then subtract the black female, which is 40. And that least may for with 210 to fill in the all other spot 25 to 64 will work the same way. I'm gonna start with my total of the bottom 2780 and then I'm just gonna work my way down the columns. So I'm gonna start with the weight males, and you could work your way up the column if you prefer. It obviously won't change the answer of the end on dhe. So I'm just gonna subtract each of the values in the column from my total. And that leaves me with 460 now again with this one because you may not have done part a yet with the over 64 um, column. I'm gonna skip down to totals so that we can fill these in with the information that we have here. So our total for the whole table is 2000 or 29,760 and then I'm going to be attracting the column, because again, if we're working on a row, we're gonna go down our columns. So I subtract the 22,050 from the top and then subtract the 4930 and then subtract the 1670 and then subtract the 330 and that leaves me with 780. And now I can use that value to figure out my over 64 with the other information that I have. So I'm gonna take the 7 80 then all of this stuff that I just calculated. So also tracked the 10 the 210 and the 4 60 So it's important to make sure those values are accurate. Um, And so I end up with 100 which is also what I got her A If you did that for the over 64 in all others column So I'm pretty sure that I didn't make any subtraction errors. They're So now we could move on to part C and calculate the probability of, um, it being on the that the randomly selected individual was a white male. So I'm gonna find the total of the white males which it tells me on the table is 22,050. And I'm going to divide that by the total in the table or the total people surveyed, which was 29,760. And when you divide that on your calculator, you get 0.74 I can do the same thing with the black females. There were 330 of those out of our total of 29,760 that were surveyed. So that calculates out to 0.11 for my total and then the probability that someone is black. Now, in this case, I have to take into consideration the black females and the black males. So the black males are 1670. The black females are 330 over the total of seven or 29,760. So when I add those together, I get 2000 over 29,760. So the probability that a randomly selected individual is black would be 0.67 and then we'll finish this question up with parts F N G Um, her F is a black or white male, so I want to find the black males are 1670 and the white males are 22,050. They haven't limited. My totals are still 29,000 760. So when I add those two together I get 23,720 over the 29,760 which gives me 0.797 for that probability. And finally the last one ass s party finds us asked us to find out if the individuals of the individuals who are over 64 find the probability that a randomly selected individual was a black or white male. So we're basically on Lee looking at that column that we filled in of the over 64 set. And so the, um, white males in the black males in that section So the black males were 140 and the white males were 4870 and our total this time is only the total for the over 64 column. In that total was 6020. So then I'm gonna take the 1 40 plus the 48 70 which is 5010 and divide by 60 20 which equals 0.83 and we're done with that question.