HP 35s User Manual page 5

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HP 35s Normal distribution applications
Now execute label D and enter the value of x for which we wish to compute the value of Q(x).
In RPN mode:
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, we'll 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 95 to enter RPN mode.
In RPN mode:
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:
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, we'll 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 95 to enter RPN mode.
In RPN mode:
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:
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Figure 10
Figure 11
HP 35s Normal distribution applications - Version 1.0