Question #47839

A local courier service reports that 90% of bulk parcels within the same city are delivered on time. Seven parcels are randomly sent to different locations.
A) What is the probability that all seven arrive on time?
B) What is the probability that exactly five arrive on time?
C) What is the probability that no more than four arrive on time?
D) Find the mean number of parcels that will arrive on time.
E) Calculate the variance of the number of parcels that will arrive on time.
F) Determine the standard deviation.

Expert's answer

A) What is the probability that all seven arrive on time: P (X = 7) = 0.9^7 = 0.478

B) What is the probability that exactly five arrive on time: P (X = 5) = 0.9^5 = 0.59

C) What is the probability that no more than four arrive on time: P (X <= 4) = P (X = 1) + P (X = 2) + P ( X = 3) + P (X = 4)

D) In the case of a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability P(x), and then adding all these products together

E) Variance measures how far a set of numbers is spread out.

F) The standard deviation σ measures the amount of variation or dispersion from the average.

B) What is the probability that exactly five arrive on time: P (X = 5) = 0.9^5 = 0.59

C) What is the probability that no more than four arrive on time: P (X <= 4) = P (X = 1) + P (X = 2) + P ( X = 3) + P (X = 4)

D) In the case of a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability P(x), and then adding all these products together

E) Variance measures how far a set of numbers is spread out.

F) The standard deviation σ measures the amount of variation or dispersion from the average.

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