According to a​ study, brain weights of men in country A are normally distributed with mean 1.37kg and standard deviation 0.13kg

Question

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

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3 months 2021-11-08T11:39:09+00:00 1 Answer 0 views 0

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.