Question

A characteristic of the Normal models is the 68-95-99.7 Rule. But when we want to work with values that don't match up with this rule, we use one of two built-in commands in the graphing calculator. The commands are normalcdf and invNorm, and to find these commands, go to 2"d DISTR and choose option 2 or 3. Notes for normalcdf: The command format is normalcdf(lower bound, upper bound, mean, standard deviation). We use this command when we are looking for a percent or probability of observing a range of data. For some problems the lower or upper bound of the range you are considering is positive or negative infinity. In these cases I recommend that you use 999999 or -999999 respectively. Please note that it is not necessary to convert values to z-scores before you use this command. Notes for invNorm: The command format is invNorm(percent of lower area of curve written as a decimal, mean, standard deviation). We use this command when we are given a lower percent or probability and we are looking for a data value. Note that the same value separates the lower 80 % from the upper 20% of values, but the command will only use the lower percent of 80 % or 0.8. Thus, if you are given an upper percent, simply subtract it from 100. Again, it is not necessary to convert any values to z-scores when applying this command. 3) Use your calculator to answer the questions below. Be sure to write the command you used and the values you entered Based on long-term investigations, researchers have suggested that the pH level of rainfall in the Shenandoah Mountains can be described by the Normal model N (4.9, 0.6). (3 points each) a) What percent of storms produce rainfall with a pH level over 6? b) What percent of storms produce rainfall with a pH level under 4? What percent of storms produce rainfall with a pH level between 3.8 and 5.5? c)

Answer 1

3)a) normalcdf(6,999999,4.9,0.774597) = 0.078

Answer : 7.8 %

3)b) normalcdf(-999999,4,4.9,0.774597) = 0.123

Answer : 12.3 %

3)c) normalcdf(3.8,5.5,4.9,0.774597) = 0.703

Answer : 70.3%