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sergejj [24]
3 years ago
9

g Q3 [20 points] Suppose that your average heart rate is 72. The average heart rate in your class is 82 and the variance is 25.

a[10 points] What percent of the class has a lower heart rate
Mathematics
1 answer:
Ganezh [65]3 years ago
7 0

Answer:

2.28% of the class has a lower heart rate

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation(which is the square root of the variance) \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 82, \sigma = \sqrt{25} = 5

What percent of the class has a lower heart rate

Lower than 72, which is the pvalue of Z when X = 72.

Z = \frac{X - \mu}{\sigma}

Z = \frac{72 - 82}{5}

Z = -2

Z = -2 has a pvalue of 0.0228

2.28% of the class has a lower heart rate

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lower bound is 25,707.48026519

Therefore the  95% confidence interval is (25,707.480 < E < 26,744.920)

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