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Sia

Question
Math
Posted 7 months ago

The distribution of resting pulse rates of all students at Santa Maria high school was approximately normal with mean μ=80\mu=80 beats per minute and standard deviation σ=9\sigma=9 beats per minute.

The school nurse plans to provide additional screening to students whose resting pulse rates are in the top 30%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
(ㄷ) 94 beats per minute
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Answer from Sia
Posted 7 months ago
Solution by Steps
step 2
Use the standard normal distribution table or a calculator to find the z-score that corresponds to the 70th percentile (since the top 30% is equivalent to the bottom 70%)
step 3
The z-score for the 70th percentile is approximately 0.52
step 4
Use the z-score formula to solve for the pulse rate XX that corresponds to this z-score: X=μ+zσX = \mu + z\sigma
step 5
Substitute the given values into the formula: X=80+0.52×9X = 80 + 0.52 \times 9
step 6
Calculate the minimum pulse rate: X=80+4.68=84.68X = 80 + 4.68 = 84.68
step 7
Round up to the nearest whole number since we are looking for the minimum rate that is in the top 30%, which gives us 85 beats per minute
B
Key Concept
Percentiles and z-scores in a normal distribution
Explanation
To find the minimum value that falls within a certain percentile of a normal distribution, we calculate the corresponding z-score and then use the mean and standard deviation to find the specific value.

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