HP 10bII+ Financial manual J7jyF, Normal Lower Tail Probability

Page 137

Normal Lower Tail Probability

To calculate the area under the curve to the left of z (the lower tail probability), enter the z-

value and press ]F. This function calculates the probability that a standard normal random variable, Z, is less than z.

Figure 5

Example

The variable Z is a standard normal random variable. What is the probability that Z is less than -1.7.?

Table 12-19 Probability example

KeysDisplay Description

\5S

.000000

Set display precision.

 

 

 

 

J7jy]F

.044565

Calculate the probability.

 

 

 

 

Figure 6

Figure 7

Statistical Calculations 129

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Contents HP Part Number NW239-90001 Edition 1, May HP 10bII+ Financial Calculator User’s GuideLegal Notice HP 10bII+ Financial Calculator Number Keyboard Map LegendTable of Contents Page Page III Basics of Key Functions JGDAt a Glance Boxed Key Functions Shift KeysJV§4 Jj7V1Percentages Add 15% toGG¼ JVÀDDà Memory KeysJ7GV GG4GV4 DSÙ JG\ÍJYÏ Time Value of Money TVMD7VÒ JyÌTVM What if How much can you borrow at a 9.5% interest rate?Amortize the 1 st through 24 th loan payments JæjgAmortization Depreciation Interest Rate Conversion Cash Flows, IRR/YR, NPV, and NFV \½\«Yj¤ Yy¤JÆG¤ GD¤Date and Calendar G7GgGJVG4 Bonds For more information on bond calculations, refer to , Bonds S7jVÎY7jVÔ Break-even \T \« \k \«\h \« \e \«YÆd¡ GÆV¡SÆJS¡ \T\«7VF \5V17GV4 ProbabilityFind Sin θ =.62 in degrees. If RAD is displayed, press 7SGTrigonometric Functions \aJg Convert the results to radians using PiAt a Glance Getting Started Power On and OffManual Conventions and Examples Displayed textItem before the / is the alternate Shift Keys JdPJG7Sg4 GY7jJ1SG7Yj4Simple Arithmetic Calculations Operating Modes1JJV7V4 Calculations in Chain ModeS7dPV7DVa 7dJ4Using Parentheses in Calculations Calculations in Algebraic ModeDa\qgVA JG\nAD4 JVyUnderstanding the Display and Keyboard Cursor Clearing the CalculatorClearing Messages AnnunciatorsClear All INV Swap Key Input KeyStatistics Keys Same as pressingD7Vj1G7DS\b Gd7GV\BMath Functions One-Number FunctionsGetting Started JVc \5YJ1SC 7DVoR\5G A7SGoRYP\ PY7V\217VdrC J7GVrcTwo-Number Functions In-line FunctionsJjÆ Jj\¨Gd\¨ Gd1DD-23below lists the two-number functions of the calculator Arithmetic with One-and Two-number FunctionsJGV\QD4 G7V\K\Qv4 VAJ7GV4GG1JY\¨ Last AnswerYV7SP \5D7JGVS4 Specifying Displayed Decimal Places\zyJG Jaj4\54 Messages D7gjSVYDBusiness Percentages GV§Business Percentage Keys Percent keyGdJ7j\¨ JGV1j§DJS7g4 JgpvæJdÀ GvvàMargin and Markup Calculations Margin CalculationsJVà Using Margin and Markup TogetherD7SÀ Using Constants Using Stored Numbers in CalculationsV1Gª Number Storage and Storage Register Arithmetic\QDª J1J§ªExample Calculate 10 + 10%, 11 + 10%, and 25 + 10% Example Calculate 23YV4 Using the M RegisterVV\¨DGª Jjs Using Numbered RegistersJY7GVm JS7dVm\w7Y ADd7JV \wG YjV7SVS7J1 V7Y\wPD YV7j \wDG7V How to approach a Financial Problem Picturing Financial ProblemsPeriods and Cash Flows Signs of Cash FlowsSimple and Compound Interest Simple InterestCompound Interest Interest RatesRecognizing a TVM Problem Two Types of Financial ProblemsCash flow diagram Borrower’s perspective Recognizing a Cash Flow ProblemCash flow diagram Investment in a mutual fund TVM Keys Using the TVM ApplicationTime Value of Money Calculations Loan Calculations Begin and End ModesJ7VÒ DpjgùJyva JVÏ1JV4 1VÌDjVyÌ 1JG4 J7VÒDDyÌ G7gÒ GV\ÚJjGVÏ Savings Calculations YgÙ1vÌ4 J7GÒ GyÏGyÌ GY\ÍYyÏ S7DÒJV\Ú Lease Calculations Cash flow diagram Calculate the monthly lease paymentJVÉ Cash flow diagram Calculate PV of the leaseGYyÌ YjÙ1vÌy4 Step Find the present value of the buy optionStep Add the results of ’ ’ and ’ ’ JVyÉ1p4 Amort key on the HP 10bII+ allows you to calculate To AmortizeJ7jVÒ Jygvï JdægyJJ7VÒ Amortize the 1st, 25th, and 54th payments GVÆVYÆ Interest Rate Conversions S7j\ÓInvestments With Different Compounding Periods First BankS7SD\Ó S7SV\ÓDS\Í Compounding and Payment Periods DifferGVyÌ DSV\ÍResetting the TVM Keys Depreciation Keys DepreciationItem in the selected format Inputs 5 for the expected useful life Depreciation example using Declining Balance Keys Cash Flow Calculations How to Use the Cash Flow ApplicationNumber1 ¤ Clearing the Cash Flow MemoryCash Flow Calculations Calculating Internal Rate of Return Vy¤Gy¤ AJG JJjSV7Gd¤NPV and IRR/YR Discounting Cash Flows Organizing Cash FlowsInitial cash flow and cash flow groups JJy¤Viewing and Editing Cash Flows 11GÆ Calculating Net Present Value and Net Future Value JVÆ1GÆ1JGyÆ1G VÆG¤ ÆY¤VÆJ¤ Æd¤ JVÆJ¤JÆJ¤ JVÒAutomatic Storage of IRR/YR and NPV Cash flow diagram Calculates NPVDate Format Calendar Formats and Date CalculationsCalendar Format Using the Input key Date Calculation Date Calculations and Number of DaysJG7JgGJJ To enter the data for this example using the Ækey\ÇJ4 ÆJ\ÇY7SGJ\Ä \5SDJ7JGJ4 J7JjGJGS7YGJV\Ä Using the ÆkeyJ7JjGJGÆ Bond Keys BondsY7GgGJ V7VÎ S7YGGJYË JJÑY7JVGJG Resetting the bond keysJ7JVGG Break-even Keys Break-evenBreak-even example Calculating the projected maximum fixed cost Resetting the Break-even keys \h\« \k\«\e\« \Z\«Entering Statistical Data Clearing Statistical DataOne-Variable Statistics Two-Variable Statistics and Weighted MeanViewing and Editing Statistical Data YD\W\5G DGÆYJV¡DVÆVJV¡ YV\W YDÆJGD¡DjÆSgV¡ Summary of Statistical Calculations D7GV¡ Y7V¡D7V¡ D7jV¡JgGÆgJ¡ JdDÆd¡JjjÆgD¡ JgVÆjj¡400 JÆdG¡ GÆJY¡DÆJJ¡ VÆGGSV¡ VÆGgd¡Weighted Mean VVÆDG¡ VÆVY¡VJÆgg¡ VJSÆdG¡Permutations Probability CalculationsFactorial VÆD VD4V9D4 VÆD9Advanced Probability Distributions YG\w6Normal Lower Tail Probability J7jyFInverse of Normal Lower Tail Probability 7GVoFStudents T Probability Lower Tail GIJ7gSy4GÆJ7gSyI Inverse of Student’s t Probability Lower Tail GSoI7V4GSÆ7VoI Conversions from Lower Tail Y1J4PG4 J7GyFReturns desired value of z Statistical Calculations \qJ1\q GaJ4 Setting a Sales PriceAdditional Examples Business ApplicationsGÆJJGJ¡ JÆJ¡DÆJDS¡ YÆJSjV¡ VÆGVd¡\q\qJ AG\n Gpdspj\qDA YVsPJ§YVjG7gy Jg§AJPJ4 Yield of a Discounted or Premium Mortgage JdyÏ VÙAYGÙG7VÒ Annual Percentage Rate for a Loan With FeesAG§Ï JSÏJGÒ AD§ÏJSaDP AJGPYV\«§4 1YVÏD7VÒ JgvïPvÙ4 JjvïJDÏ JG\ÓÉD\Ú Canadian MortgagesWhat if … TVM Calculations JJ7GÒDVVVyÌ PvÙ1 GS\ÍVÏ4 SavingsStores effective rate as annual Gains That Go Untaxed Until Withdrawal JyyùYòìï DVÙPJV§4 DyÌ G7JjVAGgCash Flow Examples Wrap-Around MortgagesGGVJ7GG Cash flow diagram Wrap-around mortgageVÌyAjVY DVy¤GG\¥ VÌy¤Low Power Annunciator Power and BatteriesInstalling Batteries Appendix a Batteries and Answers to Common QuestionsResetting the calculator Determining if the Calculator Requires ServiceCalculator won’t turn on Erasing the calculator’s memoryAnswers to Common Questions See Determining If the Calculator Requires ServiceEnvironmental Limits Equations Appendix B More About CalculationsIRR/YR Calculations Time Value of Money TVM Payment Mode Factor S = 0 for End mode 1 for Begin modeAmortization Interest Rate ConversionsCash-Flow Calculations For more than one coupon period to redemption BondsStatistics DepreciationForecasting Memory has been erased Ch Appendix C MessagesCashflow memory was cleared Tvm registers were clearedStatistical memory and registers were cleared Bond registers were clearedHP Limited Hardware Warranty and Customer Care Warranty, Regulatory, and Contact InformationLimited Hardware Warranty Period Replacing the BatteriesExclusions General TermsModifications European Union Regulatory Notice Canadian NoticeAvis Canadien Germany Customer Care Contact Information Perchlorate Material special handling may apply香港特別行 Tobago Tunisia Turkey Türkiye Turks 01-800-711-2884 ไทยWarranty, Regulatory, and Contact Information Warranty, Regulatory, and Contact Information Battery Advance payments Algebraic modeChain mode Error messages FactorialInterest rate conversions Investments In-line functions InterestKeyboard KeysWarranty Trigonometric functions TroubleshootingModes Operating modes Parentheses
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10bII+ Financial specifications

The HP 10bII+ Financial Calculator is a versatile and powerful tool designed to meet the needs of finance students, professionals, and anyone involved in financial planning and analysis. Known for its compactness and user-friendly interface, this calculator incorporates a range of features specifically tailored for financial calculations, making it an essential gadget for banking, real estate, and investment analysis.

At the heart of the HP 10bII+ is its ability to perform a wide variety of financial functions, including time value of money calculations, cash flow analysis, bond pricing, and depreciation. Its built-in functions facilitate the computation of interest rates, present and future values, net present value (NPV), internal rate of return (IRR), and annuities. This array of functionalities allows users to tackle complex financial problems with ease.

One of the standout technologies in the HP 10bII+ is its RPN (Reverse Polish Notation) input system, which allows for efficient data entry and calculation. Users can perform consecutive calculations without the need for parentheses, streamlining the process significantly. Alternatively, the calculator can also function with a standard algebraic input, catering to different user preferences.

The design of the HP 10bII+ is sleek and compact, making it highly portable and easy to handle. With a large, easy-to-read display, it ensures that users can view their calculations clearly, even in low-light environments. The keys are well-spaced and tactile, allowing for a comfortable typing experience during intensive calculations.

The calculator also offers a range of memory functions, enabling users to store and recall important values easily. This is particularly useful for financial professionals who must deal with multiple calculations and refer back to previous results frequently.

Additionally, the HP 10bII+ is powered by two AAA batteries, providing a long battery life that ensures reliability during extended use. It also features an automatic shut-off function, which conserves battery life when the calculator is not in use.

In summary, the HP 10bII+ Financial Calculator is a high-performance device that combines essential financial functions with user-friendly design and robust technology. Whether for educational purposes or professional finance work, its capabilities make it an invaluable asset for anyone dealing with financial calculations and decision-making.
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