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QI_The following are the runs scored by two batsmen Shahid Afridi and Misbah Ul Haq in ten innings. 27 20 82 45 0 13 65 14 Afridi 101 97 20 40 78 27 35 70 47 56 15 ...

Question

QI_The following are the runs scored by two batsmen Shahid Afridi and Misbah Ul Haq in ten innings. 27 20 82 45 0 13 65 14 Afridi 101 97 20 40 78 27 35 70 47 56 15 Misbah Which player is better on average and who among both is more Consistent?

QI_ The following are the runs scored by two batsmen Shahid Afridi and Misbah Ul Haq in ten innings. 27 20 82 45 0 13 65 14 Afridi 101 97 20 40 78 27 35 70 47 56 15 Misbah Which player is better on average and who among both is more Consistent?



Answers

Ben Holladay bowled 146 and 201 in his first two games. What must he bowl in his third game to have an average of at least $180 ?$

Yes. And this left no fine. A the main run and be the media run the mean is sick or to the summation of for the valleys From 1 to the last one. They were divided by one over the were divided by the number of items that we have. Yeah, add all of them. Yeah. Yeah. Yeah. Yeah, yeah. Then we divide by okay, We have 12 items. All right. Yeah. This will give us 660 over 12 And that would be 55. So the mean we are looking for. Yeah. Yes, 55 does the mean run the next one that we're looking for is the median run for media. And when I ring them, you would I ring the numbers in ascending order and look at the one that is at the center. Mhm mm. Mhm. Mhm. Yeah. Yeah. Oh. Mhm. Oh, With this one, the median. Uh huh. Yeah. Mhm. Oh, becomes the number of ice. The And on to and that's the total number of items that we have. This 12 so can number now occupies the transform to is a sick position. Plus the number that occupies the 7th position. Nevada occupies the 7th position all over to. This is because we have an every number kind of values, number of items even. So put There would be two central values instead of if we have had an odd number will be just one value. All right, So here we are looking for the set valley last seven value divided by two. Now counting 123456 So the sixes 53 7 value is 63. They were divided by two. Oh okay That is 116 on two. That is 58. So the median. Oh Or the middle value becomes 58. Thanks for your time. This is the end of the lesson.

So in this question, uh, Marcy, Rachel and Tina have all gone bowling. I mean, a little bit of information about each of their scores relatives. So we know that mercy. 100 less than twice. Rachel scores as could be twice. Rachel score minus 100. Right. So 100 less than twice. Special score. Rachel score times two minus 100. We also know that Tina, um, got 40 more than Rachel. It's a Tina, uh, equals Rachel less 40. Uh, so Tina scored equals. Rachel scored plus 40. And then the last thing we know is that Rachel scored better and mercy. So we need to figure out what the greatest score that Tina could have gotten is, um and it seems like we don't really have enough information to do that, because this is a looks, like maybe a system of equations system of linear equations in it. And we have three variables, but really only two equation. But we can We can in fact figure this out. I'm using this inequality and this, um, this equation so we know that Let me you write what I'm thinking over here, we know that our is greater than M and M equals two R minus 100. So we can rewrite this as R is greater than two are minus 100 eso. Now, if we subtract two are from both sides We get is minus R is greater than minus 100 on. Then we should multiply both sides by negative one. Right When you know that both sides by negative one that's gonna flip are, um, inequality here. So what we get is our is less than 100 s o. R. Is less than 100. We have this strictly west Stan. And because, um, when we're talking about bowling, bowling scores must be integers. We can rewrite this as our is less than or equal to 99. Right? If our is less than 100 then it's less than or equal to 99. When were constrained only two integers. So this is the greatest score that Rachel good Rachel could have a score of 99 but no higher on. And then that allows us to answer our final question. What's the highest where the Tina could have? Well, um, Tina has Rachel score plus 40 r plus 40. That's going to be less than or equal to 99 plus 40 eso the finalists get is that Tina score is less than or equal to 139. This is the greatest score a team that could possibly have given our constraints, um, that were given in the beginning of the question. Eso using this inequality are greater than M. We can find the greatest score that are, keep us we have. And then we use our third equation to find use that information to find the greatest score of the Tina could possibly.

In this problem, we are asked to compare the batting averages of two very, very excellent Baseball players. We have Williams from 1941 Who was the had the highest batting average ever, at 0.406. And then, and I believe it was the year 2000. But we're or 14 We had another player 2004. Yes, we had another player, Suzuki who had a batting average of 0.372. Mhm. We want to know who was more impressive who had the better average when compared to the averages of that time period. So again, we want to know which of these players had the better average in respect to The average for that. Again, that time period. So if we look at Williams from 1941, we're going to use our Z score formula that's shown there and we'll take his average, his batting average and subtract the average of the batting averages Which is .28062 and divide by the standard deviation Of 0.03281. So I'll get that numerator value 0.406 minus 0.28062 is 0.12538 And I'll divide that by .032 81 For AZ score of 3.82. So while that might not seem like a very high number as a Z score that is quite high. Um We usually only see Z scores up to about three standard deviations away, which means would be an easy score of three. So this is close to four. That's quite impressive. Now, if I do the same thing for The baseball player Suzuki from 2004, His batting average was 0.372 compared to the average of the averages for his time period A .26992 and a standard deviation of 0.2 154 subtracting those. Okay, I have .10208. And I'm gonna divide. Even if you don't write out this middle step, I would strongly encourage you to do this as two separate steps. Get your difference to your subtraction first, get that answer and then divide by your denominator. So Suzuki has a Z score of 4.74. So I was just saying how impressive the Williams Z score was at 3.82. But we have Suzuki even higher than that, Which means he was almost four and 3/4 standard deviations above average there. If we were to look to put these on the normal curve, they would be falling And and this is probably even if I shouldn't have done the blue. Sorry, let me fix that. If I match up here, Williams might be about there and Suzuki would be even further to the right. They would probably be even almost off of the curves. But because Suzuki has a higher Z score, his average is more impressive, also saying like his averages more extraordinary compared to the others from his time period. So that would make him the better player.

Okay, so according to the problem, the problem You that in bowler will, right? Hey, there's 70% or zero point said, hey, when you change it to decimal. Okay, so we have a probability that the bullet roots try 70%. What is the probability that the cooler will not strike so that it's actually the compliment off the probability that a ruler is trying? So that IHS one minus 0.7? Because you're so we'll be using these values there. Okay, So for the first, I think were asked to find the probably that we have three consecutive no strikes. Okay, so three, no strikes. We know that the problem team that the bowler rule that strike is your 0.3 just going to multiply zero point by itself three times since we have three consecutive games. Okay, so we have 0.3 times your point. You find your point, which is equal to zero point 0 to 7 or who converted 2%. We have 2.7%. Hey, next, pacifying the probability that Buller makes her first strike in the train. Hey, so there we have the probability that the first strike Yes, and three frame. Yeah. So the first try kiss, uh, on the first cream or first game, there will be no strike. Okay, so we have your 0.3 the second game we have most trying again. But on the third game since the first strike is in the 30 we have now 0.7. So multiplying 0.3 points times point, the times 0.0.7, we have their 0.0 16 or a 6.3%. Okay. Or letter C. What is the probability that at least was trying? There's at these ones trying in the first three frames. Hey, the letter c, the probability that a feast. Okay, one straight. Okay, so, actually, this s the compliment off. Ah, the event that there is no strike in three consecutive games that this is actually one. My Sprague will be that there's no strike in the three consecutive games. The strain, which it was already solved at this one minus your point. Yes. 0 to 7 is equal to 97 0.3. Hey, finally, okay. Were asked to find the probability that Buller will be those trying at 12 consecutive gapes. So we have child consecutive strikes may. So on the first game, we have a strike through that 0.7 the second game. We also have 0.7 strike up to the 12 K She's zero point seven also. Okay, so if we count this one, we actually have 12. 0.7. So we can actually solve this by getting zero points have been raised to 12. Okay, Which he's equal using your calculator for boxing with the zero point there. Watch the eight for because 1.38 for sense, okay?


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