texelaare

2021-08-21

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.

smallq9

Skilled2021-08-22Added 106 answers

"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$\frac{0.40}{0.98}$ :

z=-0.25

z= 2.05

The value is then the mean increased by the product of the z-value and the standard deviation.

$1=x=\mu +z\sigma =\mu -0.25\sigma$

$2=x=\mu +z\sigma =\mu +2.05\sigma$

Subtract the equations:

$1=2.30\sigma$

Divide each side by 2.30:

$0.4348=\frac{1}{2.30}=\sigma$

Determine the mean:

$\mu =1+0.25\sigma =1+0.25\left(0.4348\right)=1.1087$

Result:$\mu =1.1087.\sigma =0.4348$

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

z=-0.25

z= 2.05

The value is then the mean increased by the product of the z-value and the standard deviation.

Subtract the equations:

Divide each side by 2.30:

Determine the mean:

Result:

22+64

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