A government\'s department of transportation reported that in 2009, airline A le

Question

A government's department of transportation reported that in 2009, airline A led all domestic airlines in on-time arrivals for domestic flights, with a rate of 0.842.

Complete parts (a) through (e) below. Round to four decimal places.

a) using binomal distribution, what is the probability that in the next six flights, four will be on time?

b) using binomial distribution, what is the probability that in the next six flights, all six will be on time?

c) using binomial distribution, what is the probability that in the next six flights, at least four will be on time?

d) what is the mean? n=6

e) what is the standard deviation? n=6

Explanation / Answer

a. Assuem, X denote number of flights on time. Use, P(X,r)=nCr(p)^r(1-p)^n-r, where, p is the probability of success, n is random, independent trials, and r denote specific number of success in n trials.

P(X=4)=6C4(0.842)^4(1-0.842)^2=0.1882

b. P(X=6)=6C6(0.842)^6(1-0.842)^0=0.3563

c. P(X>=4)=1-P(X<4)=1-P(X<=3)=0.9458 [in the formul abar of EXCEL, type =1-BINOMDIST(3,6,0.842,TRUE)]

d. Mean, mu=E[X]=np=6*0.842=5.052

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