A store owner complains that, on the average, 3 bottles per case of a certain brand of softdrink are underfilled. Assuming this is correct, find the probability that a randomly chosen case of this drink will contain at least 4 underfilled bottles.
do we know how many bottles in a case?
To find the probability that a randomly chosen case of this drink will contain at least 4 underfilled bottles, we can use the concept of a binomial distribution.
First, let's define the variables:
n = number of bottles in a case
p = probability that a bottle is underfilled
In this case, the average number of underfilled bottles per case is 3. This means that the probability of a bottle being underfilled is p = 3/n.
To find the probability of having at least 4 underfilled bottles, we need to calculate the probability of having 4, 5, 6, 7, 8, 9, 10, ..., n underfilled bottles and sum them up.
The probability of having exactly k underfilled bottles in a case is given by the binomial probability formula:
P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))
where (n choose k) represents the number of ways to choose k objects out of n.
To calculate the probability of having at least 4 underfilled bottles, we need to sum up the probabilities for k = 4, 5, 6, ..., n.
P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + ... + P(X = n)
Now, you can substitute the values into the formula and calculate the probability using a binomial probability calculator or a spreadsheet software such as Microsoft Excel.