Question

html Update 3 A local courier service reports that 95% of bulk parcels within the same city are delivered within two days. Six sent to different locations. a. What is the probability that all six arrive within two Probabillity 20 Round theinwer toal b. What is the probability that exactly five arrive within two cays? (Round the final answer to 4 decimal places.) Probobility Number of parcels d-1 Compute the variance of the number that will arrive within two days. (Round the final answer to 3 decimal Veriance d-2 Compute the standard deviation of the number that will arve within two days.(Round the final answer to 4 thin two days. (Round the final answer to 4 decimal places.) Standard Deviation

Answer 1

Solution:-

Given,

P=0.95, n=6, q=(1-P)=1-0.95=0.05

it follows binomial Distribution, and is given by:-

$p(x)=\binom{n}{x}p^xq^{(n-x)}$

a.) p(x<=6)=p(x=0)+p(x=1)+.......p(x=6)

$=\binom{6}{0}(0.95^0)(0.05^(6-0))&plus;...........&plus;\binom{6}{6}(0.95^6)(0.05^(6-6))$

=0.9999 ..ans

b.)

$P(x=5)=\binom{6}{5}0.95^{5}0.05^{6-5}$

=0.2321 ...ans

c.)Mean=n*p

=6*0.95

=5.7 ...ans

d-1.)

Variance=

=6*0.95*0.05

=0.285 ..ans

d-2.)

Standard Deviation=SQRT(Variance)

=SQRT(0.285)

=0.5338 ...ans