Question related to Z score

Question

An insurance company, wants it's employees to learn a specific course. The goal is to have a participant achieve a time in the range of 30 to 45mins. Test results or 3 participants were -

Robin - with a mean time of 38mins and standard deviation of 3 mins

Alan- mean of 37mins and std dev of 2.5mins

Harold - A mean of 37.5mins with std deviation of 1.8mins

Which one should the company hire. Why?

Answer 1

Ashad

Logically, you would hire the employee who has the highest probability of 30-45 minutes. So in other words find the area between X=30 and X=45 under the standard normal distribution and take the employee with the largest area there.

I will model how to find this area for the first employee and hopefully you can follow my model for the other two.

Robin, µ = 38, σ = 3.

When X = 45, Z = (45-38)/3 = 2.33

When X = 30, Z = (30-38) / 3 = -2.67

Using Z score / area table, area to left of X=45 will be 0.9901 (Z=2.33) and area to left of X=30 will be 0.0044

So probability Robin's time is between 30 and 45 is 0.9901 - 0.0044 = 0.9857

You need to work this out for the other two and then compare the three probabilities.

Mike

Answer 2

Not so much a question about Z-score but really understanding the variability of the 3 participants.

Each participate has as overall average that falls between 30 and 45mins, however they have drastically different standard deviations.

If you reach out 3 st. dev's for Robin, part of the distribution falls outside the desired range (29, 32, 35, 38, 41, 44, 47), hence too much variation. It is possibly(unlikely but still possible) that they could complete this course outside the desired range.

If you reach out 3 st. dev's for Alan, part of the distribution falls outside the desired range. (29.5, 32,34.5,37,39.5,42,44.5). Again, slightly to much variation bc reaching 3 SD's below the avg of 37 would put you below 30mins.

If you reach our 3 st dv's for Harold, all of that distribution falls within 30 and 45mins. Giving this participant the greatest chance of falling within 30-45mins.