Question

In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of 2500 lb. Assume that the average weight of students, faculty, and staff on campus is 151 lb, that the standard deviation is 26 lb, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is to be taken: (a) What is the expected value of the sample mean of their weights? Ib (b) What is the standard deviation of the sampling distribution of the sample mean weight? (Round your answer to two decimal places.) lb (c) What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lb? (Round your answer to two decimal places.) Ib X (d) What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit? (Round your answer to four decimal places.) Pa You may need to use the appropriate table in Appendix A to answer this question. Need Help? Read Tato a Tutor 6. [-/1 Points] DETAILS PECKDEVSTAT7 8.E.021. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER An airplane with room for 100 passengers has a total baggage limit of 6000 lb. Suppose that the total weight of the baggage checked by an individual passenger is a random variable x with a mean value of 48 lb and a standard deviation of 19 lb. If 100 passengers will board a flight, what is the approximate probability that the total weight of their baggage will exceed the limit? (Hint: With n = 100, the total weight exceeds the limit when the average weight exceeds 6000/100.) (Round your answer to four decimal places.) You may need to use the appropriate table in Appendix A to answer this question. Need Help? Talk to a Tutor 7. (-/1 Points) DETAILS PECKDEVSTAT7 8.E.019. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A manufacturing process is designed to produce bolts with a 0.25-in. diameter. Once each day, a random sample of 36 bolts is selected and the diameters recorded. If the resulting sample mean is less than 0.230 in. or greater than 0.270 in, the process is shut down for adjustment. The standard deviation for diameter is 0.04 in. What is the probability that the manufacturing line will be shut down unnecessarly? (Hint: Find the probability of observing an x in the shutdown range when the true process mean really is 0.25 in. Round your answer to four decimal places.) You may need to use the appropriate table in Appendix A to answer this question Need Help? Read it Talk to a Tutor

Answer 1

b) stond ard deviation of sample mean (0.). Given Dato:- 26 n=16 l : 191 a) Expeded value of Sample meam li l =15116 6/LE = 26 VIG 2500 Sample = 6.516 mean -15625 16 X = 156.25 16 d) pla > 156.25) = P(z> -) - ples Plz > 0.8077 - 1-PC220-8047) 156.25-151 6.5 15.25 6.5 From 2- table 31-0.7904 : 0.2596 Plk 7 156.25) 20.2596 6. Given that n100 ll = HS t 19 Mean * = n ( 2 , 19°) for 100 passengers is given as follows M 19x 100 1900 P(x x > 6000] 100 48 x 100 = 4800 SOT I-plx 3 6000] Plze 1 1-P [Z¢ 0:63] 6000 - 4800 1900 From a lettle 0.26435 -1-0.73565 [P 4 2 6ccc - 16H. ASSIST

P[x > 6000] = 0.2644 7) Given Data: M=0.25 r = 0.04 X = 0.23 x=0.27 P(0.23 < 2 20.27) 0.23-0.25 0.27-0.25 3 z 004 p[-015<z2010] = P[720-5) - P[22-05) from z tolele 0.69105 - 0.3085 P(0.23<Z40*21)= 0.3830 probaleility that the manufacturing line coill Shuel.com unnecessarily is . 383.