The Town of Hertfordshire clerk knows that 23% of dogs in the town have completed emotional support training. Hertfordshire plans on showcas

Question

The Town of Hertfordshire clerk knows that 23% of dogs in the town have completed emotional support training. Hertfordshire plans on showcasing a simple random sample of its dogs in a show. Depending on which dogs are chosen, the proportion of emotional support trained dogs may vary. In a sample of 50 dogs, what is the probability that less than 6% of the dogs are emotional support trained?

Give your answer to four decimal places.

Answer: _________

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Hadley 2 weeks 2022-01-07T17:01:01+00:00 1 Answer 0 views 0

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    2022-01-07T17:02:50+00:00

    Answer:

    0.0021 is  the probability that less than 6% of the dogs are emotional support trained.

    Step-by-step explanation:

    We are given the following in the question:

    p = 23% = 0.23

    Sample size, n = 50

    \hat{p} = 6\% = 0.06

    Formula:

    z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}

    Putting the values, we get,

    z = \displaystyle\frac{0.06-0.23}{\sqrt{\frac{0.23(1-0.23)}{50}}} = -2.8564

    Thus, we have to evaluate

    P( z < -2.8564)

    Calculating the value from standard normal z-table,

    P(z < -2.8564) = 0.0021

    Thus, 0.0021 is  the probability that less than 6% of the dogs are emotional support trained.

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