Question

A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed, what range of weights would 99.7% of the dogs have?
Approximately 26–34 pounds
Approximately 24–36 pounds
Approximately 28–32 pounds
Approximately 29–31 pounds

Answer 1

Answer:

Option 2 - Approximately 24–36 pounds

Step-by-step explanation:

Given : A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed.

To find : What range of weights would 99.7% of the dogs have?

Solution :

The range of 99.7% will lie between the mean ± 3 standard deviations.

We have given,

Mean weight of Eskimo dogs is $\mu=30$

Standard deviation of Eskimo dogs is $\sigma=2$

The range of weights would 99.7% of the dogs have,

$R=\mu\pm3\sigma$

$R=30\pm3(2)$

$R=30\pm6$

$R=30+6,30-6$

$R=36,24$

Therefore, The range is approximately, 24 - 36 pounds.

So, Option 2 is correct.