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ASAP A miniature American Eskimo dog has a mean weight of 15 pounds with a standard deviation of 2 pounds. Assuming the weights of miniature Eskimo dogs are normally distributed, what range of weights would 68% of the dogs have?

Approximately 13–17 pounds
Approximately 14–16 pounds
Approximately 11–19 pounds
Approximately 9–21 pounds

Respuesta :

Answer:

Approximately 13-17 pounds.

Step-by-step explanation:

68% of the normal distribution curve is an area of about 1 standard deviation each side of the mean so the answer is  15 - 2 to 15 + 2.

luisejr77

Answer: First Option

Approximately 13–17 pounds

Step-by-step explanation:

We know that the mean weight of dogs is:

[tex]\mu = 15\ pounds[/tex]

The standard deviation is:

[tex]\sigma = 2\ pounds[/tex]

We are looking for a Z score for which it is met that:

[tex]P (-Z_0 <Z <Z_0) = 0.68[/tex]

According to the empirical rule, for a standard normal distribution it is satisfied that 68% of the data is in a range of one standard deviation above the mean and one standard deviation below the mean. This means that:

[tex]P (-1 <Z <1) = 0.68[/tex]

Then [tex]Z_0 = 1[/tex]

Therefore

[tex]\mu- \sigma<X< \mu + \sigma\\\\(15-2)<X<(15+2)\\\\13<X<17[/tex]

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