My friends & I have posted this question before but are still confused on the answer. We know the equation but the calculator part is confusing so If anyone who answers this could give an exact answer to 6 decimal places that would be great. Then we can go back & see what we were doing wrong.. Thanks
Losing your bags during airline travel is not all that uncommon. Recently, an airline was cited for losing customers' baggage 8% of the time.
A test is conducted by randomly selecting 20 customers for that airline and observing whether they had lost their baggage. Provide answers to at least 6 decimal places for the following:
The probability that at least 18 customers lost baggage is______?
To find the probability that at least 18 customers lost baggage, we need to use the binomial probability formula. The formula is:
P(X ≥ k) = 1 - P(X < k)
Where:
P(X ≥ k) is the probability of getting X at least equal to k
P(X < k) is the probability of getting X less than k
In this case, we have a binomial distribution with n=20 (number of trials/customers) and p=0.08 (probability of losing baggage for each customer).
To find the probability that at least 18 customers lost baggage:
P(X ≥ 18) = 1 - P(X < 18)
We can use a binomial probability calculator or a statistical software to calculate these probabilities.
Using a binomial probability calculator, inputting n=20, p=0.08, and k=18, we can find:
P(X ≥ 18) ≈ 0.000245 (rounded to 6 decimal places)
So, the probability that at least 18 customers lost baggage is approximately 0.000245.