Question

Assume the number of passengers (X) who order apple juice in the airplane has a Binomial distribution with p=0.1(10%) and one hundred (100) passengers are in the airplane.

a. Find average number of passengers who order apple juice (μ).
b. Find variance of the number of passengers who order apple juice (σ²).
c. Calculate P(X≤μ−3σ)

Answer 1

X represents the number of passengers who order apple juice in the airplane and follows a binomial distribution. The binomial distribution is appropriate because there are a fixed number of trials with two possible outcomes. To calculate P(X≤μ−3σ), find the value of μ−3σ and use the cumulative probability function.

Step-by-step explanation:

b. In this problem, X represents the number of passengers who order apple juice in the airplane. X is a random variable that follows a binomial distribution.

c. The binomial distribution is appropriate for this problem because there are a fixed number of trials (100 passengers) and each trial (passenger) has two possible outcomes (order apple juice or not).

d. To calculate P(X≤μ−3σ), first find the value of μ−3σ using the formulas for the mean and standard deviation of a binomial distribution. Then use the cumulative probability function to find the probability of X being less than or equal to that value.