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A sample of 25 resistors, each labeled 100 ?, had an

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 1E Chapter 5.9

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 1E

A sample of 25 resistors, each labeled 100 , had an  average resistance of 101.4\(\Omega\) with a standard deviation of 2.3 \(\Omega\). Assume the resistances are normally  distributed.

Find a 95% prediction interval for the resistance of a single resistor.  Find a tolerance interval for the resistance that in- cludes 90% of the resistors with 95% confidence.

Equation transcription:

Text transcription:


Step-by-Step Solution:
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Lecture Thirteen: Antigen Processing and Presentation  B cells can recognize antigen directly without any special requirements  T cells can recognize fragments of Ag (peptide) which is displayed in the cleft of an MHC molecule  The formation of the peptide:MHC complex requires a series of events called antigen processing, leading to the display of the antigen on the surface, which is known as antigen presentation  The T cells requirement for Ag:MHC is called MHC restriction and describes how certain T cells can only interact with one class of MHC  Measuring Helper T Cell Activity: o Can measure the proliferation or can measure cytokine production in response to an antigen  Proliferation: if you add radioactively labeled DNA to a culture, as proliferation occurs the thymidine DNA will be incorporated into the DNA being synthesized and you can proportionally gauge how much synthesis is occurring by how much radioactive DNA is present.  If you are using a dye, as synthesis occurs the dye is divided between the cells and the concentration decreases. At the end of the experiment you end up with more cells, but each containing less dye  Cytokine Production: you can assay this with a sandwich ELISA. Put an antibody down that will capture the cytokine, put the solution containing the cytokine in, and then put a marker antibody, add the substrate and the enzyme attached to the marker antibody will react with the substrate and change the solution color. Measure the color change.  Could use and ELIPSOT, this test quantifies the number of cells in a given population that are producing a cytokine  Could also stain the cytokine and then look for it with flow cytometry  Class II MHC Restriction: o Took T cells from a guinea pig and took APC (that we pulsed to present the Ag) from different donor animals. Found that the highest T helper cell proliferation resulted when the APCs and the T cells shared a common class II MHC haplotype  Mice from strain 2 (that were antigen primed) responded best to APC also from stain 2 (that were antigen pulsed) because these shared a common MHC haplotype  Mice from strain 2 did not respond to APC from strain 13 because the MHCs were not compatible.  Mice from strain 2 were able to respond to mice that were progeny (strain2/13) because these mice express both the maternal and paternal haplotypes – so these mice do express MHC with the same haplotype as the strain 2 mice. o In humans development of T cells occurs right beside APC development so the MHC molecules are the same and the T cells are able to recognize and communicate with self MHC. o ******T cells MUST have the specificity for the foreign antigen as well as the specificity for the MHC presenting it  Measuring CLT Activity: o Typically measure CD8+ activity by measuring the amount of lysis of virally infected tumor cells o Once a mice has been infected with a virus and the adaptive response has taken over, take out a cell suspension from the spleen or lymph nodes. Take this suspension (which is full of primed immune cells) and apply them to a target cell culture that has been infected with the same antigen o The primed T cells will kill the target cells containing the antigen and you can put a dye in the target cells that will leak out as the cells are killed o The amount of radioactive dye that is released into culture is proportional to the amount of killing that has occurred.  Class I MHC Restriction: o Primed spleen cells from previously infected mice and added them to dye labeled target cells. o After incubation found that the highest dye release (most killing) was observed when the CD8+ CLTS and infected target cells shared the same class I MHC haplotype.  Antigen Processing and Presentation: o For a primary humoral and cellular response induce with a native protein o For a secondary humoral response induce with a native protein o But for a secondary cellular response you could induce with a native protein or with a denatured Ag  Experiment: used a process of fixation (or freezing cells so that they are no longer metabolically active) o If the experimenters fixed the cell and then applied the antigen the cell could not take up the antigen to present it and there was no T cell activation o If the experimenters applied the antigen, waited three hours during which time the Ag was picked up and processed, and then fixed the cells there was still T cell activation o If the experimenters fixed the cells but applied already digested Ag then enough of this digested peptide replaced the regular peptides on the surface and the T cells could recognize and activate this there was T cell activation 1.) Cytosolic Endogenous Pathway: Class I MHC a. A fraction of the proteins in our cytosol are broken down and presented on our MHC. b. They are broken down by proteasomes. Immunoproteasomes are specialized for diseased cells and can break the antigen down into a specific fragment size ideal for presentation on MHC I c. The selection for which proteins are broken down is mostly random but could also be a result of ubiquitination – which is a process where a ubique protein binds to a protein and signals for it to be degraded d. TAP ½ transports proteins from the cytosol to the lumen of the RER e. MHC I binds peptide here to form a stable complex f. The MHC I is associating with chaperonins until the peptide can come along and bind g. The MHC I and peptide complex then moves to the plasma membrane through the golgi h. Plenty of association proteins that are capable of breaking up the peptide further in the RER and making it more ideal for binding MHC I- there are also plenty of associative proteins designed to help stabilize the formation of the MHCI and peptide complex 2.) Endocytic Exogenous Pathway: Class II MHC a. There is also MHC II found in the RER, but this MHCII is prevented from binding to the cytosolic peptides that are coming in to bind MHCI by an invariant chain b. The invariant chain migrates to the golgi and then intersects the endocytic pathway c. Internalized soluble proteins and membrane associated proteins are delivered in vesicles to the lysosomal compartment d. The pH drops to acidic levels and proteases digest the invariant chain leaving CLIP e. Exogenous peptides replace CLIP and the complex moves to the plasma membrane Cross presentation occurs when exogenous peptides escape their endosome and leak into the cytosol, where they are then broken down and taken to the RER with the TAP1/2 protein. They can then be presented on MHC I to cytotoxic T cells.  This is important because DC are the best at activating T cells, but in order to activate a cytotoxic T cell the Ag must be presented on MHC I (which means it must have been synthesized endogenously.) If the viral peptide doesn’t infect the DC cell and take over the cell’s machinery it would never be presented to activate cytotoxic T cells, only helper T cells. We need cytotoxic to clear the pathogen quickly. In order to present on MHC I cross presentation occurs. END OF THE CHAPTER QUESTIONS: 1.) Class I MHC is involved with endogenous proteins ( most nucleated cells have MHCI presenting peptides to cytotoxic T cells) 2.) Class II MHC is involved with exogenous proteins (APC are presenting peptides to helper t cells) 3.) Invariant chains are involved in the exogenous pathway. They prevent MHCII from binding endogenous peptides in the RER and are also involved in the movement of class II molecules from the RER to the endocytic compartments. 4.) Lysosomal hydrolases are involved in the exogenous pathway. They degrade exogenous antigens into peptides and degrade the invariant chain so that the peptides have access to the MHCII 5.) TAP 1 and TAP 2 are involved in EN (they bring the EN protein to the RER from the cytosol) 6.) Transport vesicles from the RER to the golgi are involved in both EN and EX pathway. In the EN pathway they transport peptide and MHCI complex to the golgi. In the EX pathway they transport MHCII and the invariant chain complex to the golgi and on to the endolytic compartment 7.) Proteasomes are involved in the EN pathway (break up endogenous protein in the cytosol) 8.) Endocytosis involved in EX pathway (they take in antigen from the outside in vesicles or endosomes ) 9.) Calnexin is involved in the endogenous pathway (in the RER and it helps the MHC I fold into the appropriate structure) 10.) CLIP in involved in the EX pathway (it is a remnant of the invariant chain that is left over to prevent premature peptide binding and it is replaced by the peptide to be presented) 11.) Tapasin in involved in the EN pathway and brings the TAP transporter into the proximity of class I MHC and helps peptide bind to MHC molecule Lecture Fourteen: T Cell Receptors  TCR are the arm of the T cell, they generally bind antigen that has been processed and is being presented by an APC, and they are NOT secreted. (So there is no equivalent to the B cell plasma cell.)  TCR must see the antigen in the context of an MHC with the SAME HAPLOTYPE. If the haplotypes do not match signaling or killing will not occur  Theories for MHC Restriction: o Dual Receptor Model thought that there was a TCR that recognizes the antigen and another TCR that recognizes the MHC o Altered Self Model thought that there was a single TCR that recognizes the foreign antigen complexed with the MHC (as a unit)  Experiment: With the Dual Receptor Model you would expect to see……….If you fused two T cells, the hybrid would express the MHC of T cell A and the MHC of T cell B. It would also express the receptor for antigen A and receptor for antigen B. This would be four different entities on the receptor. o They conducted a test and noticed that the fused cell didn’t have both antigen receptors , and both MHC molecules as separate entities, but expressed the partnership of MHC A and its antigen receptor as a unit and the partnership of MHC B and its antigen receptor as a unit o Concluded that the altered self model was correct  The TCR has Ig domains, with a V and a C region. On the V region there are 3 CDRS. But unlike the Ig the TCR only has two classes (alpha-beta) and (gamma-delta)  Like the Ig the TCR cytoplasmic tails do not signal  Like the Ig the Ag binding site is made up of two polypeptide chains but unlike the Ig with a heavy and a light chain, the TCR has two equal size chains  The TCR is monovalent for Ag binding  The TCR that we have studied are the alpha-beta  The gamma-delta TCR is much less popular o is sometimes found at mucosal sites o Involved in graft rejection o can recognize antigens presented by nonclassical MHC o can recognize proteins associated with tissue damage and heat shock o can be phagocytic (which is strange because T cells usually signal or lyse, they do not typically engulf)  Gene Organization: o There are fewer V regions in TCR than in Ig but there are more J sequences o The alpha region surrounds the delta region, so if the alpha region rearranges the entire delta region is spliced out o Gamma delta predominated in early life and alpha beta predominates in adult life o TCR use RAG1/2 to rearrange as well o The CDR1 and the CDR2 are already present, but the CDR3 is created during rearrangement  CDR1 and CDR2 bind to the MHC while CDR3 binds to the antigen o The constant region of a TCR anchors it into the membrane and initiates contact with the signaling complexes o The beta and delta have VDJ chains while the alpha and gamma have VJ chains o TCR can undergo rearrangement where they have VDJ or VDDJ (delta chains only) o There are a large number of ITAMS surrounding the TCR to signal to the rest of the cell  TCR Diversity: o Can undergo junctional flexibility and N nucleotide addition (more occurs if there is an extra joining of an extra D segment) o Somatic hypermutation and affinity maturation do NOT occur for TCR o Isotype switching does NOT occur o Delta genes can undergo alternative joining of D segments to form VDJ and VDDJ o In some cases the expression of an alpha chain is not excluded so some T cells express two different TCRs. This does not happen in all TCRs because the likelihood of getting a successfully rearranged alpha chain is slim as it is, let alone getting two chains  TCR Binding: o TCR can ionically interact with the CD3 (which is a signaling molecule) o CD4 is a co-receptor and it contacts the hydrophobic domains of class II MHC and the alpha and beta domains (these are conserved structures) o CD8 is a co-receptor that interacts with the alpha 2 and alpha 3 domains of class I MHC proteins (these are conserved structures) o Accessory molecules like adhesion molecules are good for strengthening and stabilizing the TCR interaction because on its own it can be weak END OF THE CHAPTER QUESTIONS 1. Antibodies directed at Ig could interact with TCR because the TCR and the Ig share a common motif, which is the immunoglobulin fold 2. The binding between TCRs and ligand is not covalent, it is mediated by ionic, van der walls, and hydrogen bonding. But the event of binding could elicit covalent binding inside the molecule (potentially through phosphorylation or cross linking between receptor molecules) 3. B cells and T cells do not have long signaling components but can still communicate because they interact noncovalenty with receptors proteins. B cells interact with Igalpha and Igbeta signaling molecules. ITAMS cover the Igalpha and the Igbeta and are activated upon antigen binding. In T cells the CD3 molcule serves this function and it equip with ITAMS.

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Chapter 5.9, Problem 1E is Solved
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Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

This full solution covers the following key subjects: resistance, Find, resistors, interval, normally. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “?A sample of 25 resistors, each labeled 100 , had an average resistance of 101.4\(\Omega\) with a standard deviation of 2.3 \(\Omega\). Assume the resistances are normally distributed.1. Find a 95% prediction interval for the resistance of a single resistor. 2. Find a tolerance interval for the resistance that in- cludes 90% of the resistors with 95% confidence.Equation transcription:Text transcription:\Omega” is broken down into a number of easy to follow steps, and 60 words. The full step-by-step solution to problem: 1E from chapter: 5.9 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 1E from 5.9 chapter was answered, more than 392 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331.

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A sample of 25 resistors, each labeled 100 ?, had an