HP 35s User Manual

							 
hp calculators 
 
HP 35s  Normal distribution applications 
 
hp calculators - 5 - HP 35s  Normal distribution applications - Version 1.0 
 Now execute label D and enter the value of x for which we wish to compute the value of Q(x). 
$
 In RPN mode:  75H/P$ 
 Figure 10 
  
Answer: The upper tail probability with a value of x equal to 20 is 0.1056. This means that 10.56% of all insurance 
adjusters would be performing faster than the individual under consideration. The person being considered 
is nearly in the top 10%.   
Example 4: Find x given a Q(x) of 0.65. Assume a standardized normal distribution. Make sure the HP 35s is in RPN 
mode.  
Solution: With the input value given as a Q(x) probability, well need to execute label I which will determine the 
appropriate value for x. Since this is a standardized normal distribution, execute label S first and enter 
values of 0 for the mean and 1 for the standard deviation. Press 9! to enter RPN mode. 
 
 In RPN mode:  7./P3P$
 
 Now execute label I and enter the value for Q(x). Note that the previous value computed for Q(x) is 
displayed at the prompt. 
$
 In RPN mode:  7;/DRMP$  
 Figure 11 
 
Answer: The value of x for which the upper tail probability is equal to 0.65 is –0.3853. Since the normal distribution 
is symmetrical around the mean, 50% of the area / probability will be above the mean and 50% will be 
below the mean. In this example, since we were looking for a value of x for which upper tail probability 
would be 65%, the value of x would be have to be less than 0.  
Example 5: The average number of claims processed per hour by an insurance adjuster is 15 with a standard deviation 
of 4 and follows the normal distribution. Within what range, evenly distributed on either side of the average, 
would you expect to find 50% of the adjusters performing?  
Solution: With the input value given as a Q(x) probability, well need to execute label I which will determine the 
appropriate value for x. Since this is a not a standardized normal distribution, execute label S first and enter 
values of 15 for the mean and 4 for the standard deviation. Press 9! to enter RPN mode. 
 In RPN mode:  7.3MPQP$
 
 Now execute label I and enter the value for Q(x). Note that the previous value computed for Q(x) is 
displayed at the prompt. 
$
 In RPN mode:  7;$   
						

							 
hp calculators 
 
HP 35s  Normal distribution applications 
 
hp calculators - 6 - HP 35s  Normal distribution applications - Version 1.0 
 Were looking for a range within which 50% of the probability falls that is evenly spread around the average. 
Since the normal distribution is symmetrical, this means that 25% would be below the mean and 25% 
would be above the mean. The input values for Q(x), however, are upper tail probabilities. This means the 
values of Q(x) that need to be input will be 0.75 and 0.25. 
 
 In RPN mode:  /DHMP$  
 Figure 14 
 
 In RPN mode:  7;/DSMP$  
 Figure 15 
 
Answer: The middle 50% of the adjusters would average processing between 12.3020 and 17.6980 claims per hour.    
						

							 
 
hp calculators 
 
 
 
 
HP 35s  Linear Regression 
 
 
 
 
Linear Regression 
 
Practice solving linear regression problems 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
hp calculators 
 
HP 35s  Linear Regression 
 
hp calculators - 2 - HP 35s  Linear Regression - Version 1.0 
Linear Regression 
 
Linear regression calculates the equation for a line that best fits a set of ordered pairs by minimizing the sum of the 
squared residuals between the actual data points and the predicted data points using the estimated line’s slope and 
intercept. The equation of the line produced by linear regression is in the form Y = mX + b, where m is the slope of the 
line and b is the Y-intercept. Once the slope and intercept have been calculated, it is fairly easy to substitute other values 
for X and predict a corresponding value for Y, or to substitute a value for Y and predict a value for X. When the X value is 
a measure of time (months or years, for example), the equation is specifically referred to as a trend line.  
 
On the HP 35s, values are entered into the statistical / summation registers by keying in the number (or pair of numbers) 
desired and pressing !. This process is repeated for all numbers or pair of numbers.  When entering a pair of 
numbers in RPN or algebraic mode, key the Y value, press , then key the X value and press !.  
 
To view the linear regression results, press #$. The HP 35s displays a menu of relevant values. Items on this 
menu are viewed by pressing the % or & cursor keys of the HP 35s. 
 
This menu allows you to predict a value for X given a Y value, or predict a value for Y given an X value. It also displays 
the linear regression lines correlation, slope, and y-intercept. The correlation will always be between –1 and +1, where 
values closer to –1 and +1 indicating a good “fit” of the line to the data. Values nearer to zero indicate little to no “fit.” 
Little reliance should be placed upon predictions made where the correlation is not near –1 or +1. Exactly how far away 
from these values the correlation can be and the equation still be considered a good predictor is a matter of debate. To 
use a value displayed on the menu, press the  button and the value will be copied for further use. This is 
illustrated in the problems below. 
 
Practice solving linear regression problems 
 
Example 1: What is the slope and y-intercept of the line that best fits the points (0,4), (2,5) and (3,6)? 
 
Solution: Be sure to clear the statistics / summation memories before starting the problem.  
 ()*
 
 In RPN or algebraic mode: 
 
 )+!,-!./!*
  
 To view the linear regression results, press #$. Figure 1 displays the menu shown.*
 
 Figure 1 
 
 In either RPN or algebraic mode, press: &&&to view the slope. 
 
 Figure 2 
 In either RPN or algebraic mode, press: & to view the y-intercept.   
						

							 
hp calculators 
 
HP 35s  Linear Regression 
 
hp calculators - 3 - HP 35s  Linear Regression - Version 1.0 
 
 Figure 3 
 
Answer: The slope of the line is 1 and the y-intercept is 3. The linear regression equation is Y = 1 X + 3. 
 
Example 2: What is the slope and y-intercept of the line that best fits the points (2,5), (4,10), (6,20), and (9,25)?  
 What is the correlation? Is the linear regression line a good fit to the data points? 
 
Solution: Be sure to clear the statistics / summation memories before starting the problem.  
 ()*
 
 In RPN or algebraic mode: 
 
 ,-!+0)!-0.!-,1!*
 *
 To view the linear regression results, press #$. Figure 4 displays the menu shown. 
 
 Figure 4 
 
 In either RPN or algebraic mode, press: &&&to view the slope. 
 
 Figure 5 
 
 In either RPN or algebraic mode, press: & to view the y-intercept. 
 
 Figure 6 
 
 In either RPN or algebraic mode, press: %% to view the correlation. 
 
 Figure 7 
 
Answer: The slope of the line is 2.991 and the y-intercept is –0.701. The linear regression equation is  
 Y = 2.991 X – 0.701. The correlation value of 0.9783 indicates a very good fit of the linear regression line 
 to the data points. It is a good fit. 
   
						

							 
 
hp calculators 
 
 
 
 
HP 35s  Working with Fractions 
 
 
 
 
 
 
 
Simple Examples Using Fractions 
 
Fractions in Programs and Equations 
 
Exact Control of Fraction Display 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
hp calculators 
 
HP 33S  Working with Fractions 
 
hp calculators - 2 - HP 33S  Working with Fractions - Version 1.0 
Simple Examples Using Fractions 
 
The HP 35s allows the user to enter numbers as fractions of the form “a b/c”, to view results as fractions, and to control 
the way fractions are displayed. The symbol “a b/c” is written below the decimal point on the keyboard as a reminder that 
this key is used for most operations with fractions. Four simple examples will show the basics. 
 
Example 1: Add 1 ¾ to 2 ! 
 
Solution: The decimal point is used for fraction entry as follows. 
 
 In RPN mode, type the number 1 and press the decimal point key to separate the fractional part from the 
integer part. Then type 3, and the calculator will display 1.3. Press the decimal point key again and the 
calculator will recognize that a fraction is being entered. Press the number 4 and the calculator will display 
the fraction, as in Figure 1. 
 
 Figure 1 
 
 Now press then press the ! key, then type the number 2 ! in the same way. Finally add the two. 
The keystrokes for the whole calculation are as below. 
 
 #$#%!&##()*
 
 Figure 2 
 
 In algebraic mode, enter the numbers in the same way, but press the plus key between the two numbers. 
 
 #$#%)&##(!*
 
 Figure 3 
 
Answer:  The result is 4  and is displayed as a decimal number; the HP 35s recognizes numbers that are entered 
as fractions, but displays numbers as decimals unless told to display them as fractions. 
 
Example 2: Display the result of the above calculation as a fraction. 
 
Solution: Both in RPN mode and in algebraic mode, press +, for fractional display of numbers. 
 
 +,*
 
 Figure 4   
						

							 
hp calculators 
 
HP 33S  Working with Fractions 
 
hp calculators - 3 - HP 33S  Working with Fractions - Version 1.0 
Answer:  The result, 4  is now displayed as a fraction; the display of Figure 3 will change to that in Figure 4. , 
is on the front of the decimal point key, which is also used for entering fractions. 
 
Example 3: Display the result using only halves, thirds or quarters. 
 
Solution: The - key allows the user to select the largest value allowable for the “/c” part of a fraction “a b/c”. If the 
number 4 is stored in - then only fractions with 2, 3 or 4 on the lower part (the denominator) will be 
displayed. 
 
 In RPN mode, type 4 and then press .- to see the previous result displayed as a fraction using only 
halves, thirds, or quarters. 
 
 %.-*
 
 Figure 5 
 
 The number 4 3/8 is displayed, rounded to 4 1/3. 
 
Answer:  If the fraction  must be approximated as the nearest fraction with 2, 3 or 4 in the denominator, then the 
closest value is 1/3. A small up-arrow symbol is shown at the right of the display, informing the user that the 
real answer is slightly larger than the answer displayed. The number 4 1/3 is 4.33333333333 to the 
accuracy of the HP 35s, but the true number is 4 3/8, or 4.375 exactly. To show the exact value, 
./ must be pressed. Like ,, - is above the decimal point key, which is also used for 
entering fractions. 
 
Example 4: Round the actual result to be the result displayed. 
 
Solution: As the example above showed, the value is not altered when the fraction display is changed. , is a 
display mode, much like FIX or ENG, which also change the way a number is displayed, but not its true 
value. To change the true value to be as close as possible to that displayed, the RND (number round) 
command must be used. 
 
 Type +0 to round the result to the decimal representation of the fraction being displayed. Do not 
confuse 0 with the 1 (random number) command. 
 
 +0*
 
 Figure 6 
 
Answer:  Pressing ./ shows that the decimal value has been rounded to 4.33333333333, which is the 
closest possible value to 4 1/3. 
 
 The small arrow now points down, to show that the exact decimal value is smaller than the fraction 
displayed. This is because 4.33333333333 is just smaller than 4 1/3.   
						

							 
hp calculators 
 
HP 33S  Working with Fractions 
 
hp calculators - 4 - HP 33S  Working with Fractions - Version 1.0 
 To restore - to its largest possible value, press 2.-. The largest possible value is 4095. 
 
 To stop showing numbers as fractions, press +, a second time. 
 
Fractions in Programs and Equations 
 
When an equation is typed in, numbers cannot be typed as fractions. Instead, they should be typed using the division 
symbol. For example, 1 1/3 can be typed as (1 + 1 ! 3). Better still is to type it as 4 ! 3. 
 
Example 6: Enter the equation D + 1 1/3 
 
Solution: As explained, 1 1/3 is best typed into an equation as 4/3. 
 
 345)%6$! 
 
 Figure 7 
 
Answer:  The expression D + 1 1/3 is entered as the equation D + 4 ! 3. 
 
Note: the command , cannot be stored in a program. Instead of this, flag 7 should be set to display fractions, and 
cleared to return to normal display of numbers. See below for information about flags. 
 
Exact Control of Fraction Display 
 
Example 4 showed that - can be used to control how fractions are displayed, through control of the denominator. 
 
Normally, in , mode, fractions are displayed to be as close as possible to the true value. The only limitation is that 
the denominator “c” can be no larger than 4095. 
 
If a number smaller than 4095 is stored in - then the largest possible value of “c” is that number, but any possible 
value of “c” can be used. 
 
If flag 8 is set, then the numerator must be exactly “c”, but the fraction can be simplified. If flag 8 is set and flag 9 is set 
too, then the numerator must be exactly “c”, and there is no simplification. 
 
Example 7: Display the fraction 179/3000 using the different flag settings combined with -. 
 
Solution: This example will be shown in RPN mode. The same steps work in algebraic mode, but that +7 is 
needed after each step when a flag is changed, as in example 3 above. First enter the fraction, and make 
sure - is set to 4095, which is its usual value.  
 
 2#89#$222!2.-*
 
 Figure 8