Sampling Distribution. This week's problem is inspired a student I'll be working with this week. Statistics presents itself in various subjects outside of mathematics. A common topic of students learning statistics is computing and using a z-score. A z-score helps to standardize data so that probabilities related to that data can be found...at least that's how my brain 🧠 thinks about it. Age, salaries, test scores, etc. If it can quantified and certain other information (mean and/or standard deviation) about the data is known, then you may be able to find and use z-score. ...And you know what that means...word problems! 😩
To solve this week's problem in completion, you need to recall the following math skills:
✔️ How to calculate the z-score
✔️ How to use a Normal probability table
Here is WMP! #42:
Check back on Friday, March 19th for the solution, which will be posted below ⬇️.
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✏️📓 Solution Time! 📓✏️
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Alright, alright. Because word problems can be annoying, I always advise to identify the information in the problem that you will be using to solve it. So, here is my color-coded version of the problem, highlighting the important information:
Next, we'll use the highlighted information, above, in the z-score formula. The only way we'll be able to find the probability of interest is to standardize the values of interest. Since there are two values of interest, we compute two z-scores. This will allow us to use a Normal probability table.
Now that we have the two z-scores we need, we can find probability of interest. You can definitely use a wide variety of software and probability calculators to obtain the answer. I used a couple and will share those screen shots soon. First, let's use a Normal probability table. There are many to choose from. The table I linked has a simple display, but you still need to understand the symmetrical aspect of a Normal curve to use it.
The problem asked for "the probability that the average blood pressure...will be between 118 and 124 mmHg." Because we standardized the data, we can look at this as the probability between the z-scores -0.4 and 0.2
One of our z-scores is negative and the other is positive. The Normal table being used here only shows positive z-scores. Here is where the beauty of the symmetrical nature of the Normal curve is helpful. I will "switch" the negative z-score with its positive counterpart so that I can use the probabilities from the table.
As promised, here are a few screen shots of online probability calculators I used that confirmed the answer above:
So to answer the question... The probability that the average blood pressure of this sample will between 118 and 124 mmHg is 0.2347. 👍🏿
▪️ How did you go about finding the probability?
▪️ Leave your response down below and let me know what you thought about this week's problem.
Thanks for solving with me this week!
Up next WMP! #43. 👩🏿🏫
Cheers!
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