Questions: The probability of flu symptoms for a person not receiving any treatment is 0.054. In a clinical trial of a common drug used to lower cholesterol, 63 of 1066 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that at least 63 people experience flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the drug? (a) P(X ≥ 63)=0.2514 (Round to four decimal places as needed.) (b) What does the result from part (a) suggest? A. The result x ≥ 63 is significantly high, so the result suggests that the drug increases the likelihood of flu symptoms. B. The result x ≥ 63 is not significantly high, so the result suggests that the drug has no effect on flu symptoms. C. The result x ≥ 63 is significantly high, so the result suggests that the drug has no effect on flu symptoms. D. The result x ≥ 63 is not significantly high, so the result suggests that the drug increases the likelihood of flu symptoms.

The probability of flu symptoms for a person not receiving any treatment is 0.054. In a clinical trial of a common drug used to lower cholesterol, 63 of 1066 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that at least 63 people experience flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the drug? (a) P(X ≥ 63)=0.2514 (Round to four decimal places as needed.) (b) What does the result from part (a) suggest? A. The result x ≥ 63 is significantly high, so the result suggests that the drug increases the likelihood of flu symptoms. B. The result x ≥ 63 is not significantly high, so the result suggests that the drug has no effect on flu symptoms. C. The result x ≥ 63 is significantly high, so the result suggests that the drug has no effect on flu symptoms. D. The result x ≥ 63 is not significantly high, so the result suggests that the drug increases the likelihood of flu symptoms.
Transcript text: The probability of flu symptoms for a person not receiving any treatment is 0.054 . In a clinical trial of a common drug used to lower cholesterol, 63 of 1066 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that at least 63 people experience flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the drug? (a) $P(X \geq 63)=0.2514$ (Round to four decimal places as needed.) (b) What does the result from part (a) suggest? A. The result $x \geq 63$ is significantly high, so the result suggests that the drug increases the likelihood of flu symptoms. B. The result $x \geq 63$ is not significantly high, so the result suggests that the drug has no effect on flu symptoms. C. The result $x \geq 63$ is significantly high, so the result suggests that the drug has no effect on flu symptoms. D. The result $x \geq 63$ is not significantly high, so the result suggests that the drug increases the likelihood of flu symptoms.
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Solution

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Solution Steps

Step 1: Calculate the Probability of Exactly 63 Successes

Using the binomial probability formula:

\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{n-x} \]

where:

  • \( n = 1066 \) (total number of people treated),
  • \( x = 63 \) (number of people experiencing flu symptoms),
  • \( p = 0.054 \) (probability of flu symptoms without treatment),
  • \( q = 1 - p = 0.946 \) (probability of not experiencing flu symptoms).

The calculated probability of exactly 63 successes is:

\[ P(X = 63) = 0.0398 \]

Step 2: Calculate the Probability of At Least 63 Successes

To find the probability of at least 63 successes, we first calculate the cumulative probability of having fewer than 63 successes:

\[ P(X < 63) = \sum_{i=0}^{62} P(X = i) \]

After calculating the probabilities for \( i = 0 \) to \( 62 \), we find that:

\[ P(X < 63) \approx 0.7486 \]

Thus, the probability of at least 63 successes is:

\[ P(X \geq 63) = 1 - P(X < 63) = 1 - 0.7486 = 0.2514 \]

Step 3: Interpret the Result

The probability \( P(X \geq 63) = 0.2514 \) indicates that the occurrence of at least 63 people experiencing flu symptoms is not significantly high. This suggests that the drug does not have a substantial effect on increasing the likelihood of flu symptoms.

Final Answer

The results suggest that the drug has no effect on flu symptoms, leading us to conclude:

\[ \boxed{B} \]

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