Question

The response time for ski patrol rescue responders is measured by the length of time from when the radio call is finished and when the responders locate the skier. Responders consider between 0 to 5 minutes as an ideal response time.

Supposing gathered data showed a Normal distribution with a mean of 6 minutes and standard deviation of 1.2 minutes, what percent of responses is considered ideal? Round to the nearest whole percent.
Use the z-table to answer the question.

Answer 1

Explanation:

Since this distribution is normal,

we can use the z score formula.

z=(x-μ)/σ

Where x is some random value we choose

Where μ is the mean(6)

Where σ is the stdev(1.2)

We need to find values between the times x=0 and x=5, which is considered ideal so let use two z scores.

When x=0:

`(0-6)/(1.2) =-5\\`

This is a z score of -5, this is VERY,VERY, unlikely to occur so this percentage can be considered 0%

When x=5:

`(5-6)/(1.2) =-0.83`

Using the z score table, we get a percentage about 20.33%

Since the z score gives us a percentage of data is left of the point of interest , we subtract the larger percentage- smaller percentage

20.33%-0= 20.33%= 20%

So about 20% percent of the responses is considered ideal.