z-Score Question

[lokimotii]

Hello, my professor has a habit of creating really unique word problems that differ immensely from the textbook problems. I am curious if anyone can help me tackle this one?

In pharmacologic research a variety of clinical chemistry measurements are routinely monitored closely for evidence of side effects of the medications under study. Suppose typical blood-glucose levels are normally distributed, with mean = 90 mg/dL and standard deviation = 38 mg/dL.
If the normal range is 65-120mg/dL, then what probability/proportion/relative frequency of values will fall below the normal range, and above the normal range?

 

[Harry_the_cat]

I would start with a sketch of a normal curve and shade in the appropriate area you need to find. Can you show when you have done that?

 

[Dr.Peterson]

Hello, my professor has a habit of creating really unique word problems that differ immensely from the textbook problems. I am curious if anyone can help me tackle this one?

In pharmacologic research a variety of clinical chemistry measurements are routinely monitored closely for evidence of side effects of the medications under study. Suppose typical blood-glucose levels are normally distributed, with mean = 90 mg/dL and standard deviation = 38 mg/dL.
If the normal range is 65-120mg/dL, then what probability/proportion/relative frequency of values will fall below the normal range, and above the normal range?

There's something I want to point out to you about your question, which may help you in general.

You say that this is an example of "really unique word problems that differ immensely from the textbook problems". The fact is, this problem is almost certainly almost identical to examples you have seen, in terms of what is called its "deep structure". You appear to be focusing on the "surface structure", that is, what it is talking about on the surface (pharmacological research, which you may know nothing about, and therefore feels totally foreign), and missing the fact that it is really just a basic problem in disguise. To solve such a problem, you have to first "take off the mask" so you can recognize it!

If I take out the non-mathematical words and replace them with letters, here is what is left:

Suppose X is normally distributed, with mean = 90 mg/dL and standard deviation = 38 mg/dL.​

What probability/proportion/relative frequency of X will fall below the normal range, 65-120 mg/dL, and above the normal range?​

One thing I recommend when you start a problem is to extract the key facts from the paragraph into a little table:

Mean = 90​

Standard deviation = 38​

Goals: proportion less than 65, proportion greater than 120​

Does clearing away the underbrush help you find your way through this a little more easily? Am I right that you have seen questions like "what percent will fall below 65?" before?

For a nice short introduction to the idea of deep structure, see here. The book referred to sits on the shelf next to me ...

 

[lokimotii]

There's something I want to point out to you about your question, which may help you in general.

You say that this is an example of "really unique word problems that differ immensely from the textbook problems". The fact is, this problem is almost certainly almost identical to examples you have seen, in terms of what is called its "deep structure". You appear to be focusing on the "surface structure", that is, what it is talking about on the surface (pharmacological research, which you may know nothing about, and therefore feels totally foreign), and missing the fact that it is really just a basic problem in disguise. To solve such a problem, you have to first "take off the mask" so you can recognize it!

If I take out the non-mathematical words and replace them with letters, here is what is left:

Suppose X is normally distributed, with mean = 90 mg/dL and standard deviation = 38 mg/dL.​

What probability/proportion/relative frequency of X will fall below the normal range, 65-120 mg/dL, and above the normal range?​

One thing I recommend when you start a problem is to extract the key facts from the paragraph into a little table:

Mean = 90​

Standard deviation = 38​

Goals: proportion less than 65, proportion greater than 120​

Does clearing away the underbrush help you find your way through this a little more easily? Am I right that you have seen questions like "what percent will fall below 65?" before?

For a nice short introduction to the idea of deep structure, see here. The book referred to sits on the shelf next to me ...

Thank you so much!!

 

[lokimotii]

I would start with a sketch of a normal curve and shade in the appropriate area you need to find. Can you show when you have done that?

I now finished the assignment the problem was on but do have the work if you're curious and thank for suggesting!