Question

Math

Posted 5 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
```

Sign in to unlock the answer

Answer from Sia

Posted 5 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.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question