According to a study, brain weights of men in country A are normally distributed with mean

1.37kg and standard deviation 0.13kg. Apply the empirical rule to complete each sentence. Complete parts (a) through (c).

a. Complete the sentence "Approximately 68% of the men have brain weights between kg and kg."
b. Complete the sentence "Approximately 95% of the men have brain weights between kg and kg
c. Complete the sentence "Approximately 99.7% of the men have brain weights between kg and kg

a) "Approximately 68% of the men have brain weights between 1.24 kg and 1.50 kg."

b) "Approximately 95% of the men have brain weights between 1.11 kg and 1.63 kg

c) "Approximately 99.7% of the men have brain weights between 0.98 kg and 1.76 kg

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 = 1.37kg

Standard deviation = 0.13kg

a. Complete the sentence "Approximately 68% of the men have brain weights between kg and kg."

By the Empirical Rule, within 1 standard deviation of the mean.

1.37 - 0.13 = 1.24kg

1.37 + 0.13 = 1.50kg.

b. Complete the sentence "Approximately 95% of the men have brain weights between kg and kg

By the Empirical Rule, within 2 standard deviations of the mean.

1.37 - 2*0.13 = 1.11kg

1.37 + 2*0.13 = 1.63kg.

c. Complete the sentence "Approximately 99.7% of the men have brain weights between kg and kg

By the Empirical Rule, within 3 standard deviations of the mean.

1.37 - 3*0.13 = 0.98kg

1.37 + 3*0.13 = 1.76kg.

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