Question

The distribution of resting pulse rates of all students at santa maria high school was approximately normal with mean μ = 80 beats per minute and standard deviation σ = 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?

Answer 1

The minimum resting pulse rate at Santa Maria High School for students who will receive additional screening is approximately 84.716 beats per minute.

Step-by-step explanation:

To find the minimum resting pulse rate at Santa Maria High School for students who will receive additional screening, we need to calculate the z-score corresponding to the top 30% of the distribution. First, we find the z-score using the formula: z = (x - µ) / σ, where x is the resting pulse rate, µ is the mean (80 beats per minute), and σ is the standard deviation (9 beats per minute). In this case, we want to find the z-score that corresponds to an area of 0.3 in the upper tail of the normal distribution. Using a standard normal distribution table or a calculator, we find that the z-score corresponding to an area of 0.3 is approximately 0.524.

Next, we solve for x in the z-score formula: x = z * σ + µ. Plugging in the values, we have x = 0.524 * 9 + 80. Simplifying, we find x ≈ 4.716 + 80. Therefore, the minimum resting pulse rate for students who will receive additional screening is approximately 84.716 beats per minute.