Final answer:
To estimate the probability that at least 38 people experienced flu symptoms in a clinical trial, you can use the binomial distribution and calculate the probability using the cumulative distribution function (CDF). This result suggests a possible association between the drug and the increase in flu symptoms.
Step-by-step explanation:
To estimate the probability that at least 38 people experienced flu symptoms in a clinical trial, we need to use the binomial distribution. The probability of flu symptoms for a person not receiving any treatment is given as 0.035. We can calculate the probability of exactly 38 people experiencing flu symptoms using the binomial formula, and then calculate the probability of 38 or more people experiencing flu symptoms by summing up the probabilities of 38, 39, 40, and so on up to the total number of people treated.
a. To estimate the probability that at least 38 people experienced flu symptoms, we can use the cumulative distribution function (CDF) of the binomial distribution. If X is the number of people experiencing flu symptoms, we want to find P(X >= 38). Calculate the probability of 37 or fewer people experiencing flu symptoms using the CDF, and subtract it from 1 to get the probability of 38 or more people experiencing flu symptoms.
b. This result suggests that the drug might have an effect on the likelihood of flu symptoms. The observed number of people experiencing flu symptoms (38) is significantly higher than expected based on the probability of flu symptoms for a person not receiving any treatment (0.035). It indicates a possible association between the drug and the increase in flu symptoms.