Assume the resting heart rates for a sample of individuals are normally distributed with a mean of 75 and a standard deviation of 5. Use the 68-95-99.7 rule to find the following quantities.

a. The relative frequency of rates less than 85 using the 68-95-99.7 rule is .
b. The relative frequency of rates greater than 80 using the 68-95-99.7 rule is .
c. The relative frequency of rates between 65 and 75 using the 68-95-99.7 rule is .

This question is based on the standard deviation. Therefore, the answers are: (a)  0.975, (b) 0.16  and (c) 0.475.

It is given that assume the resting heart rates for a sample of individuals are normally distributed with a mean of 75 and a standard deviation of 5. Use the 68-95-99.7 rule to find the following quantities.

We know that,

The Empirical Rule states that, for a normally distributed random variable are as follows:

68% of the measures are within single standard deviation of the mean.

95% of the measures are within two standard deviation of the mean.

99.7% of the measures are within three standard deviations of the mean.

In this problem,  

Mean = 75

Standard deviation = 5

Now, the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above.

a. The relative frequency of rates less than 85 using the 68-95-99.7 rule is

85 is the two standard deviations above the mean.  So, all the 50% below the mean is below 85.

And of the 50% above the mean, 95% is less than 85.  

So, 0.5 + 0.95*0.5 = 0.975

b. The relative frequency of rates greater than 80 using the 68-95-99.7 rule is

80 is one standard deviations above the mean of the 50% above the mean, 68% is less than 80. So, 100-68 = 32% is more than 80.

c. The relative frequency of rates between 65 and 75 using the 68-95-99.7 rule is

The mean and two standard deviations below the mean.

So, 95% of 50%

Therefore, the answers are: (a)  0.975, (b) 0.16  and (c) 0.475.

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a) 0.975

b) 0.16

c) 0.475

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 75

Standard deviation = 5

We also have that since the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above.

a. The relative frequency of rates less than 85 using the 68-95-99.7 rule is

85 is two standard deviations above the mean.

So all the 50% below the mean is below 85

And of the 50% above the mean, 95% is less than 85. So

0.5 + 0.95*0.5 = 0.975

b. The relative frequency of rates greater than 80 using the 68-95-99.7 rule is

80 is one standard deviations above the mean.

Of the 50% above the mean, 68% is less than 80. So 100-68 = 32% is more than 80.

0.32*0.5 = 0.16.

c. The relative frequency of rates between 65 and 75 using the 68-95-99.7 rule is

Within the mean and two standard deviations below the mean.

So 95% of 50%

0.95*0.5 = 0.475

answer: 3.26019516

step-by-step explanation:

a

step-by-step explanation: