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

Question

According to a study, brain weights of men in country A are normally distributed with mean 1.55 kg and standard deviation 0.16 kg. Apply the empirical rule to complete each sentence. Complete parts (a) through (d) a. Complete the sentence "Approximately 68% of the men have brain weights between kg. Appraimately 68% of the men have ban weights between | | kg and 1 kg. Type integers or decimals. Do not round) b. Complete the sentence "Approximately 95% of the men have brain weights between-_ kg and--kg Approximately 95% of the men have brain weights between 11 kg and L /kg. Type integers or decimals. Do not round) c. Complete te sentence "Approximately 99.7% of the men have brain weights between kg and Appro omately 99.7% of the men have brain weights between and L kg. Type integers or decimais. Do not round) d. Graph the areas enclosed by each set of values in parts (a) through (c) Graph the area enclosed by the values in part (a) O A. ??. O C. O D. Graph the area enclosed by the values in part (b) O A. O B. O C. O D. Graph the area enclosed by the values in part (c) O A. ??. O C. O D.

Explanation / Answer

According to the 68 – 95 – 99.7 thumb rule, 68%, 95% and 99.7% of values in a data set lies within 1, 2 and 3 standard deviations of mean respectively.

Mean 1.55 kg

Standard deviation = 0.16 kg

a)      1.55 – 0.16 = 1.39 kg

1.55 + 0.16 = 1.71 kg

Approximately 68% of the men have brain weight between 1.39kg and 1.71 kg

b)      1.55 – 2x0.16 = 1.23 kg

1.55 + 2x0.16 = 1.87 kg

Approximately 95% of the men have brain weight between 1.23 kg and 1.87 kg

c)       1.55 – 3x0.16 = 1.39 kg

1.55 + 3x0.16 = 1.71 kg

Approximately 99.7% of the men have brain weight between 1.07 kg and 2.03 kg

d)      1. Graph B

2. Graph C

3. Graph A

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