PINWORM INFESTATION COMMONLY FOUND IN KIDS CAN BE TREATED WITH THE DRUG PYRANTEL PAMOATE. RESEARCH SHOWS THE TREATMENT IS EFFECTIVE IN ABOUT 90% OF CASES. DRUG IS ADMINISTERED TO 25 KIDS
WHAT IS THE PROBABILITY THAT EXACTLY 23 OF THEM ARE CURED?
WHAT IS THE PROB. THAT MORE THAN 23 OF THEM ARE CURED?
WHAT IS THE PROB. THAT AT MOST 23 OF THEM ARE CURED?
WHAT IS THE EXPECTED # OF KIDS THAT WILL BE CURED USING THIS TREATMENT?
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To answer these questions, we need to apply the binomial distribution formula. In this case, the probability of success (curing the pinworm infestation) is 0.9, as research shows that the treatment is effective in about 90% of cases. The number of trials is 25 since the drug is administered to 25 kids.
1. Probability that exactly 23 of them are cured:
We can use the binomial probability formula: P(X=k) = (nCk) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success, and ^ represents exponentiation. For this problem, we want k to be 23.
P(X=23) = (25C23) * (0.9)^23 * (1-0.9)^(25-23)
To calculate P(X=23), we need to determine (25C23), which represents the number of ways we can choose 23 out of 25 kids.
(25C23) = 25! / (23!(25-23)!) = 25! / (23!2!)
Using the formula, we can calculate P(X=23) as:
P(X=23) = (25C23) * (0.9)^23 * (0.1)^2
2. Probability that more than 23 of them are cured:
We need to find the probability that 24 or 25 kids are cured. To calculate this, we sum the probabilities of P(X=24) and P(X=25).
P(X>23) = P(X=24) + P(X=25)
3. Probability that at most 23 of them are cured:
We need to find the probability that 23 or fewer kids are cured. To calculate this, we sum the probabilities of P(X=0) through P(X=23).
P(X<=23) = P(X=0) + P(X=1) + ... + P(X=23)
4. Expected number of kids that will be cured:
The expected number, denoted as E(X), is calculated as the sum of the products of each possible outcome multiplied by its corresponding probability.
E(X) = sum(k * P(X=k)) for all possible values of k
Therefore, we can use this formula to calculate the expected number of kids that will be cured by the treatment.
Note: Calculating the values for P(X=k) and P(X<=k) require knowing the mathematical operation of combination (nCr), exponentiation (^), and factorial (!).