8. By one estimate, 3% of all Siberian Husky puppies are born with two different colored eyes (called heterochromia iridum). For rando

Question

8. By one estimate, 3% of all Siberian Husky puppies are born with two different
colored eyes (called heterochromia iridum). For random samples of 50 Siberian
Husky puppies, what are the mean and standard deviation of the number of
puppies that will have two different colored eyes?

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Valentina 2 weeks 2022-01-11T00:48:10+00:00 1 Answer 0 views 0

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    2022-01-11T00:49:50+00:00

    Answer:

    Mean = 1.5

    Standard Deviation = 1.206

    Step-by-step explanation:

    Percentage of Siberian Huskies with two different colored eyes = p = 3% = 0.03

    Sample size selected = n = 50

    We have to find the mean and standard deviation of the number of puppies with two different colored eyes.

    Either the puppies will have two different colored eyes or they won’t. Sample size is fixed in this case which is 50. A puppy with two colored eyes is independent of other puppies, this means the trials are independent. The probability of success is fixed in this case which is 3%. This setting satisfies all 4 conditions of a Binomial experiment, so we will use the formula relevant to Binomial experiment to answer this question.

    Mean number = \mu=np

    Using the values, we get:

    \mu=50(0.03)=1.5

    Standard deviation of Binomial experiment is calculated as:

    \sigma=\sqrt{np(1-p)}

    Using the values, we get:

    \sigma=\sqrt{50 \times 0.03 \times 0.97}\\\\ \sigma=1.206

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