Suppose that the probability that a new medication will cause a bad side effect is 0.03. If this medication is given to 150 people, what is the probability that more than three of them will experience a bad side effect?
The probability is 4.5 people.
To find the probability that more than three people will experience a bad side effect, we can use the binomial probability formula. The binomial probability formula is given by:
P(X = k) = nCk * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability that exactly k successes occur,
n is the number of trials,
k is the number of successes,
p is the probability of success in each trial, and
nCk is the number of combinations of n items taken k at a time.
In this case, we want to find the probability that more than three people will experience a bad side effect. So, we need to calculate the probabilities for k = 4, 5, 6, ..., 150, and then sum them up.
Let's calculate each individual probability using the formula:
P(X > 3) = P(X = 4) + P(X = 5) + P(X = 6) + ... + P(X = 150)
Using the binomial probability formula, and given that the probability of a bad side effect is 0.03 (p = 0.03), the number of trials is 150 (n = 150), and k goes from 4 to 150, we can calculate each term of the summation and then add them up. This can be done using a calculator or a statistical software.
Alternatively, you can use online calculators, statistical software, or programming languages with built-in functions to calculate the cumulative probability directly.