So to solve this problem, we're going to need to calculate four different T scores. One for each, um, specific number of minutes that we're looking at stone part. They were looking at the probability that somebody does less than 17 minutes. I used X to represent the number of minutes that they dio or do use the stair climber. So probability that it's less than 17 minutes. So we need a Z score for 17 minutes. Part B. We're looking for between 20 and 28. We need to one for 20 and one for 28 for part C, we're gonna need one for 30. I get dizzy score. We can use this formula. So Z score for 17 minutes, be given as X minus mu. So exes are 17 minus mu, which is the population, I mean, which is given us 20 just We divide all of that by the standard deviation, which is five Consol. This to find that disease scored 17 is negative 170.6. Now we do the same thing for a next see score. So the Z score for 20 minutes would be using the same formula. We're just gonna plug in 20 instead of 17. So right in that red bubble we're gonna put 20 instead. And then we calculated again we should get zero z score for 28 plugging in 28th this time. Okay, calculate that and you should get a C score of 1.6 and then our Z score for 30 should be too. So here's our Z scores. Oops, These air Z scores and now we can use them to find these probabilities. So each of these three scores represents of Mark on our standard normal curve. So our first the score of negative 0.6, we fall somewhere like here and then the corresponding value on RZ table represents the area to the left or the probability of a value being less than this value. So we look up negative 0.6 on RZ table. You should get points to seven. So 0.27 is the probability that somebody does less than 17 minutes. That's our answer for a part B is a little bit more complicated. Now we're looking for what's between two values. We have our first one, which again the corresponding values could be everything to its left. We also have a second one. And again, the corresponding value on RZ table will be everything to the left of that. Since we just want this middle section, we're going to take the corresponding value for our higher value. Sorry. 28. We're gonna take the course the Z score for the 28. So 1.6 and its corresponding probability, which again is going to cover this entire area to the left, all that green, and then we're subtracting off the same thing. But for are last year values. So the Z score of 20 everything to the left of that and that should just give us a middle region. This is just a generalized picture because the Z score of zero would actually line up or like here. But this gives you the general concept. So we look up our 1.6 on our, um, de table. You should get a probability of 0.945 and then we look up, are devalue for 20 on the Z table, and you should get a probability of 200.5 source subtracting 0.5. Then you can compute that, and you should get a probability of 0.445 and that's our answer for Part B. And then for part C, this is gonna be similar to part A. Except this time we want the area to the right instead of to the left, because we're looking for things that are greater than rather than less than because this represents a probability we're still gonna have our line. And normally the corresponding value gives us the area to the left. The probability that that it's less than that because we're working with probability, we can just do one minus this value, and that should give us the opposite, which is everything to the right instead, and that's what we're looking for. So we have our one minus, and then we look up our Z score or Z score for thirties to look up to on RZ table or again. You can use a graphing utility. You should get 0.977 We have one minus 10.977 gives us 0.0 to 3, and that's the probability that somebody's on the climber for more than 30 minutes.