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

Question

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

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the minimum resting pulse rate for the top 30%, we need to determine the z-score that corresponds to the 70th percentile of a standard normal distribution. ‖ ‖ 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.⚹◊What is the z-score formula used to calculate the minimum resting pulse rate for students qualifying for additional screening?⍭ Generate me a similar question◊

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