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​Women's heights average 62 inches with a standard deviation of 2.9 inches in a certain study. Use the​ 68-95-99.7 rule to determine the typical ranges of the​ women's heights. In what range will approximately the middle 95​% of the​ women's heights​ lie?

Respuesta :

dogacandu

Answer:

Middle 95​% of the​ women's heights​ lie between 59.1 inches and 64.9 inches

Step-by-step explanation:

According to the 68-95-99.7 rule ,

  • 1 standard deviation around the mean includes middle 68% of the population
  • 2 standard deviation around the mean includes middle 95% of the population
  • 3 standard deviation around the mean includes middle 99.7% of the population

Therefore Middle 95​% of the​ women's heights​ lie 62±2.9 inches according to the study. That is between 59.1 inches and 64.9 inches.

raphealnwobi

68% are within 59.1 to 64.9 inches, 95% are within 56.2 to 67.8 inches and 99.7% are within 53.3 to 70.7 inches

What is empirical rule?

The empirical rule states that for a normal distribution, 68% of the values falls within one standard deviation from the mean, 95% of the values falls within two standard deviation from the mean and 99.7% of the values falls within three standard deviation from the mean.

Mean = 62 in, standard deviation = 2.9 in

68% are within 62 ± 2.9 = (59.1, 64.9)

95% are within 62 ± 2 * 2.9 = (56.2, 67.8)

99.7% are within 62 ± 3*2.9 = (53.3, 70.7)

68% are within 59.1 to 64.9 inches, 95% are within 56.2 to 67.8 inches and 99.7% are within 53.3 to 70.7 inches

Find out more on empirical rule at: https://brainly.com/question/10093236

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