Luggage checked-in at Airline A arrives on time to its intended destination with a probability of 0.63. In a random sample of 2000 bags, what would be the mean number of bags (out of the 2000) that arrive on time to its intended destination. Also find the standard deviation. Group of answer choices

The mean number of bags that arrive on time to its intended destination is 1260 with a standard deviation of 21.59.

Step-by-step explanation:

For each bag, there are only two possible outcomes. Either it arrives on time to it's intended destination, or it does not. The probability of a bag arriving on time is independent of other bags. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

Luggage checked-in at Airline A arrives on time to its intended destination with a probability of 0.63.

This means that

In a random sample of 2000 bags

This means that

Mean and standard deviation of the number of bags that arrive on time to its intended destination:

The mean number of bags that arrive on time to its intended destination is 1260 with a standard deviation of 21.59.

Step-by-step explanation:

for A

for B