Question 243ptsThe starting salary ofan administrative assistant is normally distributed with a mean of $50,000 and a standard deviation of $2,500. We know that the...

As shown in Example $6.12,$ incomes of junior executives are normally distributed with a standard deviation of $\$ 3828.$ a. What is the mean for the salaries of junior executives, if a salary of $\$ 62,900$ is at the top end of the middle $80 \%$ of incomes? b. With the additional information learned in part a, what is the probability that a randomly selected junior executive earns less than $\$ 50,000 ?$

In question About 28 Does something mean is normally distributed those mean and standard diffusion? The justice score is a very decreased by the new, divided by the standard deviation, which was equal to 63 and 400 thousands minus 65,010. 700 mhm 14,500 over square root off 48 with equal to one negative. 1.10 to do. To remind the corresponding probability using table for so probability you fix This is done 63 1004 100 dollars equal to P Oh said less than negative 14 in 10. Pretty equal to all 0.13 57 which is equal to 13.75 Person. I've got to find him. Answer. Thank you.

Your question. Number 27. The sample mean is normally distributed with me. You understand? Your division said over a square Root off that easy score is the value decreased by them, divided by the standard diffusion so that the school is equal to X minus mu over signal over square root of in which would equal to 6, 60 thousands, minus 66 solvents over 12,000 over square root off 35 which is equal to negative to a point 96 Determined the correspondent Probability. Using a table four mhm. We'll fix this them 60 thousands dollars equal to probability off his head. This is them negative. 2.96 physical to four point double. 0 15. But equal to all points 15%. And that the ends for this question. Thank you.

Right in this problem. We have two parts, even a and A B part, and both parts are centered around the fact that we have an average teacher salary. So we're talking about the population of teachers in Connecticut having an average salary of 57,000 $337 and the standard deviation is $7500. So we're going to use that in both huts. So let's focus on part A and in part A. We want the probability that a teacher one teacher has an A salary that's less than $52,000 a year. So with that, we're going to have to draw a bell curve. And with the bell curve, we always put the average in the center. So we're gonna have 57,000 337 in the center, and we're looking for on average or s aureus salary less than 52,000. So the next thing we're gonna have to do is we're going to have to calculate the Z score associated with 52,000, So we're going to 52,000 minus 57,337 divided by the standard deviation of 7500 and the Z score associated with the 52,000 is approximately negative 0.71 So what we can do is we can go back to our picture, and we could say that 52,000 is equivalent to a Z score of negative 0.71 So we can also rewrite our problem to say the probability that the Z score is less than negative 0.71 sear, then going to use your standard normal distribution chart in the back of your textbook. And when we look up negative 0.71 we're going to get a value of point 2389 So for part a, the probability that a teacher selected has a salary of less than $52,000 would be 0.2389 Now let's go to Part B and in Part B. We're going to use the same information about the population, and we know that the average salary of the teacher in Connecticut was 57,337 and the standard deviation was 7500. But in part B, we're now going to select a sample of teachers and in this instance were selecting 100 teachers. So our sample size is 100 and we now want to find out what the probability is that the sample mean of those 100 is less than $56,000. So since we have a sample of 100 we're talking sample means the central limit theorem is going to go into play. And according to the Central Limit Theorem, the average of the distribution of means will be the same as the average of the population, which in this case is 57,300 37. And the standard error of the means is going to be the standard deviation of the population divided by the square root of the sample size. And again, in this case, it's going to be 7500 divided by the square root of when, So we're going to want to draw another bell curve, and again we're gonna put the average in the center, and 56,000 is gonna be over here. And we're looking for, on average to be less than 56. That was so we need to find busy score, associate it with 56,000. So our Z score is going to be 56,000 minus 57,300 37 divided by the standard deviation of those means with standard error of the mean, which is our Sigma, or the 7500 divided by the square root of 100. And that turns out to be approximately negative 1.78 So we can now go back to our picture. And we could say that the Z score associated with 56,000 is negative 1.78 so we can rewrite our problem instead of us talking about the probability that the average is less than 56,000. We can talk about the probability that the Z score is less than negative 1.78 So we're then going to go to our standard normal distribution chart in the back of the book, and we're going to find the probability to be 0.375 So in summary, Part B was asking us what's the probability that when we select 100 teachers, their average salary is less than 56,000 and the answer would be 0.3 75

Were asked to find the probability that a randomly selected teacher turns between $80,000 so they can express. That is the probability that teacher and 35 spend 25,000 dollars a year. And we're given that the average annual salary. Uh, you, too. 47 dozen. So 50 others. That is just delicious trends that we can use from season two. Thanks. This you signal were also given signal or the standard deviation is equal to it doesn't 686 today we're gonna attempt this problem is to find the Z value spertus for these separate conditions. 5000. Perfect. So let's set this one C one this on C two Dan, we're gonna get is Z one is equal to 35 1000. Nice. You? Which is? I have 7 7050 over signal. That doesn't 600 a. I mean, this value is equal to negative 2.24 Now again to the same thing for easy to see to Jersey. Going to 45 dozen minus said 50 to first 1006 100 18. Go Mean that that is in a cool negative zero four eight. So now that we have this, we can rewrite this original expression as from Billy the negative, too. 24 Just Z value for that doesn't is less than Jeanne just less than negatives. You for eight. Now, what we're gonna do is check out the Z table, find the corresponding probabilities of these values for negative 2 to 4. Get your print you to five for natives, use for bait. Digging is your point three, but six. So now we condemn view it. This as follows as the probability that Z is less than negatives your point for and minus the probability that C is less than neck It is, too to four. We know that this is the same thing. Is this so you can just put that and share substitute values in 05 six minus You're sure 12 Which gives us ju 2.3. You're to me. What? That's fine. Apart. Be slightly different. It's asking us probability that teacher earns more than $40,000 a year so you can write. That is the probability that eggs is greater done. 40 1000 dollars. So to solve this, we're just going to use the same from love. Just Z is equal to extra for signal. We know that mule and sing Listen Same useful 50 signal respect in 680. So if you just go ahead substitute 40,000 50 uh, 6 5080 80. They're gonna get value off negative one point 36 However, I usually use this formula distance to be less than inside. And since it's not have toe do one minus, we're gonna have to do probability of said this crater 1.36 is equal to one, minus the probability probability. I see it's less than negative one from 36 That is the equivalent statement. And it's it's useful for us to write it like this because, okay, we can find this value right here using this formula and just one minus to get greater than questions. So now if you find the corresponding value for negative 36 from our see table, we're going to get zero a six. But so done. Iffy. Substitute back into here. Get one minus is your hey six, which is the corresponding probability to this. See value on that gives us a final answer. Serial 0.9 one one for Part C. The question is asking us that if you were offered there you $1000 a year for this position, how would you feel basic information? And so there's no there's no real calculation. You need to do this for this part, but you just need to look at your parts A and B on used logical thinking to terminate. Answer. So here we can tell that the probability that a teacher earns more than $40,000 a year is open 9131 which is the same thing as 91 0.3 1%. No 1.1% of teachers more than $40,000 a year. Therefore, if you were offered doing so 31 dozen dollars, you wouldn't be too happy because most teachers would be making a lot more than you