Question

A local courier service reports that 70% of bulk parcels within the same city are delivered within two days. Six parcels are randomly sent to different locations.

a. What is the probability that all six arrive within two days? (Round the final answer to 4 decimal places.)

Probability   

b. What is the probability that exactly five arrive within two days? (Round the final answer to 4 decimal places.)

Probability   

c. Find the mean number of parcels that will arrive within two days. (Round the final answer to 2 decimal place.)

Number of parcels   

d-1. Compute the variance of the number that will arrive within two days. (Round the final answer to 3 decimal places.)

Variance   

d-2. Compute the standard deviation of the number that will arrive within two days. (Round the final answer to 4 decimal places.)

Standard Deviation

Answer 1

Given the probability that the bulk parcels within the same city are delivered within two days is 0.70.

Six parcels are randomly sent to different locations.

Let X be the number of parcels delivered within two days.

Therefore

a) The probability that all six arrive within two days is given by:

b)

The probability that exactly five arrive within two days is given by:

c) The mean number of parcels that will arrive within two days is given by:

The mean number of parcels that will arrive within two days are 4.20

d1) The variance of parcels that will arrive within two days is given by

The variance of parcels that will arrive within two days is 1.26

d2) The standard deviation of parcels that will arrive within two days is given by

The standard deviation of parcels that will arrive within two days is