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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: _________

Respuesta :

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

[tex]\hat{p} = 6\% = 0.06[/tex]

Formula:

[tex]z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

Putting the values, we get,

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

Thus, we have to evaluate

P( z < -2.8564)

Calculating the value from standard normal z-table,

[tex]P(z < -2.8564) = 0.0021[/tex]

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

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