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In a harvest of pumpkins, the mean diameter of the pumpkins is 21 inches with a standard deviation of 5 inches. The diameters are normally distributed, so 95% of the pumpkins fall within a certain range of values around the mean. Select the pumpkins that fall into this range.

Respuesta :

Answer:

Here are the pumpkins that fall into the 95% range:

Pumpkin Diameter (inches)

11.20 - 30.80

Step-by-step explanation:

Answer:

The diameter of the 95% pumpkins should be between 11 and 31 inches.

Step-by-step explanation:

For Empirical Rule (68 - 95 - 99.7 rule):

which means

  • 68% of the population falls within -1 to 1 standard deviation
  • 95% of the population falls within -2 to 2 standard deviation
  • 99.7% of the population falls within -3 to 3 standard deviation

Since the question is 95%, which means the size of the pumpkins should be: [tex]\boxed{mean\ \pm\ 2\ standard\ deviation}[/tex]

[tex]=21\pm2(5)[/tex]

[tex]=21\pm10[/tex]

[tex]=11\ inches < diameter < 31\ inches[/tex]