Standard deviation with only a mean and a percentage value.

[BaalHacks]

I ask alot of questions on here and I hope not to annoy. Since my questions deal with obscure problems hopefully it will make it so others don't have to ask in the future. Anyway I need to calculate the standard deviation in a question with only a mean and a value. Example:

The life span of a DVD player produced by one major company is known to be normally distributed with a mean of 6.2 years. If 4.01% of these DVD players have a life span of more than 8 years what is the standard deviation of the DVD players life span?

I am interested in finding out how to solve a question like this. I haven't found and examples like this in my text or on the internet.

If anyone knows how to solve this please teach me.

[Outlier]

The Z score translates between standard deviation and percent of cases above or below a given percentage of cases.

[BaalHacks]

Could you give me an example?

[Dason]

The Z score translates between standard deviation and percent of cases above or below a given percentage of cases.

Note that there are special cases where it wouldn't work... For instance if you were given that 50% of the values fell below 6.2 then you still wouldn't be able to solve for the standard deviation.

[SPR]

Hello Baalhacks,

Z-score = (x-m)/s, where x-life span, m-mean life span, s-standard deviation of life span. x > 8 tanslates to z-score > z0, where z0 corresponds to probability 0.0401. Table or calculation gives z0=1.7495. Ssubstituting this z0 into the first formula gives s=1.0288. Note that when using table for z-score it is necessary to see values for probability (1-0.0401).

Sincerely,
SPR

[miriam]

Hello Baalhacks,

Z-score = (x-m)/s, where x-life span, m-mean life span, s-standard deviation of life span. x > 8 tanslates to z-score > z0, where z0 corresponds to probability 0.0401. Table or calculation gives z0=1.7495. Ssubstituting this z0 into the first formula gives s=1.0288. Note that when using table for z-score it is necessary to see values for probability (1-0.0401).

Sincerely,
SPR

I am working on this question, I am confused as to where I find the Standard deviation to input into the formula????