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Suppose Siri (an Apple digital assistant) is known to answer general facts correctly approximately 20.94% of the time. If a consumer asked Siri 200 questions about general facts, what is the probability that less than 20.43% of them would be correct

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Olajidey

Answer:

Probability = 0.4297

Step-by-step explanation:

Given that,

p = 20.94% = 0.2094

1 - p = 1 - 0.2094 = 0.7906

n = 200

[tex]\mu\hat p = p = 0.2094\sigma\hat p = \sqrtp ( 1 - p ) / n[/tex]

[tex]\sigma\hat p = \sqrt (0.2094 * 0.7906) / 0.02877[/tex]

[tex]P( \hat p < 0.2043) =[/tex]

[tex]P(( \hat p - \mu\hat p ) / \sigma\hat p < (0.2043 - 0.2094) / 0.02877)[/tex]

[tex]= P(z < -0.1771)= 0.4297[/tex]

Probability = 0.4297

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