Question

For the general population of adults, typing speed on an iPad touch keyboard is normally distributed with a mean of 30.6 words per minute (wpm) and a standard deviation of 14.1 wpm. A temporary staffing agency is trying to fill several administrative jobs with various touch keyboard typing speed requirements.

An applicant with the staffing agency has an iPad typing speed of 25 wpm. What percent of adults have a typing speed of less than 25 wpm?

Answer 1

`P(X<25)=P((X-\mu)/(\sigma)<(25-\mu)/(\sigma))=P(Z<(25-30.6)/(14.1))=P(z<-0.397)`

And we can find this probability with the normal standard table or excel and we got:

`P(z<-0.397)=0.346`

And that correspond to 34.6 % approximately

Explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the typing speed of a population, and for this case we know the distribution for X is given by:

`X \sim N(30.6,14.1)`

Where
`\mu=30.6` and
`\sigma=14.1`

We are interested on this probability

`P(X<25)`

And the best way to solve this problem is using the normal standard distribution and the z score given by:

`z=(x-\mu)/(\sigma)`

If we apply this formula to our probability we got this:

`P(X<25)=P((X-\mu)/(\sigma)<(25-\mu)/(\sigma))=P(Z<(25-30.6)/(14.1))=P(z<-0.397)`

And we can find this probability with the normal standard table or excel and we got:

`P(z<-0.397)=0.346`

And that correspond to 34.6 % approximately