What is the probability that all six arrive within two days? (Round the final an

Question

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

    

     

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

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

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

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

1. A local courier service reports that 88% of bulk parcels within the same city are delivered within two days. Six parcels are randomly sent to different locations.

Explanation / Answer

X ~ Binimial(n,p) = Binomial (6,0.88)

P(X) = nCx px (1-p)n-x

a)

P( X = 6) = 6C6 0.886 0.120

= 0.4644

b)

P(X = 5) = 6C5 0.885 0.121

= 0.3800

c)

Mean = np = 6 * 0.88 = 5.28

d)

Variance = np(1-p)

= 6 * 0.88 * 0.12

= 0.634

e)

Standard deviation = sqrt(np(1-p))

= sqrt( 6 * 0.88 * 0.12)

= 0.7960

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