Question

question
a certain cold remedy has an 82% rate of success of reducing symptoms within 24 hours. find the probability that in a random sample of 50 people who took the remedy, 35 of them had a reduction of symptoms within a day.

• round your answer to three decimal places.

provide your answer below:

Explanation:

Step1: Identify binomial parameters

$n=50$, $k=35$, $p=0.82$, $q=1-p=0.18$

Step2: Calculate combination term

$\binom{n}{k} = \binom{50}{35} = \frac{50!}{35!(50-35)!} = 225082957510$

Step3: Compute success/failure terms

$p^k = 0.82^{35} \approx 0.000377$, $q^{n-k}=0.18^{15} \approx 1.4901\times10^{-11}$

Step4: Multiply all terms

$\binom{50}{35} \times p^k \times q^{n-k} \approx 225082957510 \times 0.000377 \times 1.4901\times10^{-11}$

Step5: Round to 3 decimal places

$0.001$

Answer:

0.001