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The brain volumes ​(cm cubedcm3​) of 20 brains have a mean of 1189.81189.8 cm cubedcm3 and a standard deviation of 126.5126.5 cm cubedcm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such​ data, would a brain volume of 1432.81432.8 cm cubedcm3 be significantly​ high?

Respuesta :

Answer:

Lower limit = 936.8

Upper limit = 1442.8            

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 1189.8 cube cm

Standard Deviation, σ = 126.5 cube cm

Range rule of thumb:

  • The range rule of thumb says that the range is four times the standard deviation.

[tex]\text{Range} = 4\times 126.5 = 506[/tex]

  • The range rule of thumb suggests that most values would be in the area covered by four standard deviations that is within two standard deviations above or below the mean.

Lower limit =

[tex]\mu - 2\sigma\\= 1189.8 - 2(126.5)\\ = 936.8[/tex]

Upper limit =

[tex]\mu + 2\sigma\\= 1189.8 + 2(126.5)\\ = 1442.8[/tex]

Thus, most values lie within (936.8,1442.8)

A brain volume of 1432.8 cube cm is not significantly high because it is less than the upper limit.

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