Question

Math

Posted 4 months ago

```
The distribution of resting pulse rates of all students at Santa Maria high school was approximately normal with mean $\mu=80$ beats per minute and standard deviation $\sigma=9$ beats per minute.
The school nurse plans to provide additional screening to students whose resting pulse rates are in the top $30 \%$ of the students who were tested.
What is the minimum resting pulse rate at that school for students who will receive additional screening?
Choose 1 answer:
A) 76 beats per minute
(B) 85 beats per minute
(C) 87 beats per minute
D) 89 beats per minute
(E) 94 beats per minute
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 2

Using the standard normal distribution table or a calculator, we find that the z-score for the 70th percentile is approximately 0.52

step 3

We can now use the z-score formula to find the corresponding pulse rate: $z = \frac{X - \mu}{\sigma}$, where $X$ is the pulse rate, $\mu$ is the mean, and $\sigma$ is the standard deviation

step 4

Solving for $X$ gives us $X = z \cdot \sigma + \mu$. Substituting the values, we get $X = 0.52 \cdot 9 + 80$

step 5

Calculating the value of $X$, we find that the minimum pulse rate is $X = 4.68 + 80 = 84.68$ beats per minute

B

Key Concept

Percentiles and z-scores in a normal distribution

Explanation

To find a specific percentile in a normal distribution, we use the z-score that corresponds to that percentile and then translate it back to the original scale using the mean and standard deviation.

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