The amount of time Ricardo spends brushing his teeth follows a Normal distribution with unknown mean and standard deviation. Ricardo spends less than one minute brushing his teeth about 40% of the time. He spends more than two minutes brushing his teeth 2% of the time. Use this information to determine the mean and standard deviation of this distribution.

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smallq9 · Accepted Answer

&quot;Table A contains the probabilities to the left of a z-score or for values smaller than z-score    The time is less than one minute about 40% of the time.     The time is more than two minutes about 2% of the time and thus less than two minutes about 98% of the time.    The z-value is then the value in the table A corresponding to a probability of 0.400.98 :                                z=-0.25                                                            z= 2.05                                The value is then the mean increased by the product of the z-value and the standard deviation.                 1=x=μ+zσ=μ−0.25σ                                  2=x=μ+zσ=μ+2.05σ                   Subtract the equations:                              1=2.30σ                              Divide each side by 2.30:                               0.4348=12.30=σ                               Determine the mean:                 μ=1+0.25σ=1+0.25(0.4348)=1.1087                Result:μ=1.1087.σ=0.4348

The amount of time Ricardo spends brushing his teeth follows a Normal distribution with unknown mean

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