So let us look at this question. Now, the incubation tank are approximately normally distributed with a standard deviation of one day and mean as 21 days. Okay, so the mean happens to be 21 days and standard deviation is one day. Right? So this is 21 Sigma Standard Division is one. All right. Now, what is the probability that a randomly selected fertilized chicken egg hatches in less than 20 days? Less than 20 days? Okay, so we know the formula Z is equal to X minus mu by sigma. What is X? In this case, this is part a 20. So this is 20 minus move, which is minus one upon one, which happens to be minus one. So my Z statistic, my that statistic is minus one. Okay, now what do I do? I find the p value so my Z score is minus one. Great. This is one tail. You can either use a set table or you can use an online package like or any other statistical package like our or excel, which will give you, uh, the value that is exact and quite quickly. So p values 0.15 86 Okay, so, Mike, P value for this corresponding. That statistic is point 1586 Okay, so what is the probability that a randomly selected fertilized chicken and hatches in less than 20 days it is going to be 200.1586? All right, moving on. But visas? What is the probability that randomly selected for daylight you can takes over 22 days to hatch. Oh, shape. Let us look at this. Now, my ex is 22. My ex is 20 to 22 now, this is movie moved on to part B 20 to minus 20 by one, which happens to be too. So why is that statistic now? Is to I find the p value or two. Okay, I hit on calculate and I get 0.2 275 My P value turns out to be 2750.2275 So what is the probability if we read the question again? Okay. What is the probability that are randomly selected? Fertilized chicken egg takes more than 22 days to hatch. It is going to be the answer that we found. That is 0.2275 And if I want to find the probability that the egg will hatch in less than 22 days, right, 22 or less number of days, it will be one minus 0.0 to 75. Okay, so if I use my calculator for this, this is going to be one minus 0.2275 which is 0.97725 0.97725 Alright. Now moving on to part C. What is part C have to say, What is the probability hatches that the egg hatches between 19 and 21 days. Okay, 19 and 21 days. So let's just look at the diagram. The mean happens to be 2019 is going to be somewhere around here, right? This is going to be 19 and 21 will be somewhere around here. What we want is the probability in between. Okay, so what I do is I find the P value for 19 and find the P value for 20. And that is the areas in the teens, right? These two areas and I subtract both of them from one. So this is going to be one minus the P value of 19 minus the P value of 21. Okay, so if I put 19, this is going to be my Zach statistic. Turns out to be minus one for 21. My, that statistic turns out to be one. Okay, so if I find the p value for this, the value for both of them is going to be the same, because both of them are one away. One standard deviation away. Right? So my p values 0.1586 So p value is 0.1586 So disk reason is 1586 and this region is also 0.1586 So which means I have to do one minus twice off 0.1586 which is 0.6828 So this 0.6828 This is my answer for part C, where my probability that my ex is between 19 and 21 days. Yeah. Okay. What is part D? Would it be unusual for an act to hatch in less than 18 days? Yes. The probability that an egg hatches in less than 18 days is unusual because this is less than two standard deviations away, right? 18 is less than two standard deviations away. If this is 18, this is 20. This is 18. So this less than 18 means this This is less than two standard deviations of it. So this is going to be less than 2.5%. Okay, between 2.5 to 5% of the area. So yeah, this is rare. This is unusual.