Acor ing to an arine, fights on acertain route are on time 85% of the time. Supp

Question

Acor ing to an arine, fights on acertain route are on time 85% of the time. Suppose 10ights are randomly selected and menum berofont me fights isrecord (a) Explain why this is a binomial experiment. (c) Find and interpret the probability that fewer than 7 fights are on time. (d) Find and interpeet the probablity that at least 7 flights are on time. (e) Find and interpeet the probability that between 5 and 7 flights, inclusive, are on time. (a) Identify the statements that explain why this is a binomial experiment Select all that apply A. The experiment is performed until a desired number of successes is reached B. There are two mutually exclusive outcomes, success or failure. C. Each trial depends on the previous trial. D. The trials are independent. E. The probability of success is the same for each trial of the experiment. are three mutually exclusive possibly outcomes, armiving on-time, arriving early, and arriving late G. The expenment is performed a fixed number of times Click to select your answers) and then click Check Answer romairing Clear A ·F& 2 4 0 s lock M.

Explanation / Answer

a)A binomial experiment is a statistical experiment that has the following properties:

The experiment consists of n repeated trials.

Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.

The probability of success, denoted by P, is the same on every trial.

The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.

From above points options are B,D,E,G

Refer below table for calculating next answers

Here, n =10, p = 0.85, q= 1-p= 0.15

2nd last couln indicates probability corresponding to x value in column 1

whereas last column is addition of all probabilities till that value of x

b)P(exactly 7 flights are on time) = P(when x=7) = 0.129

c)P(fewer than 7 flights are on time)= P(x=1)+..P(x=6) = 0.049

d)P(atleast 7 flights are on time)= P(x=7)+P(x=8)+P(x=9)+P(x=10)

= 0.129+ 0.276 + 0.374 + 0.197 = 0.95

e)P(between 5 to 7 flights on time) = P(x=5)+P(x=6)+p(x=7)

= 0.008+0.04+0.1298 = 0.178

X nCx P^x q^n-x nCx.P^x.q^n-x Cummulative
addition 1 10 0.85 3.84434E-08 3.26769E-07 3.26769E-07 2 45 0.7225 2.56289E-07 8.3326E-06 8.65937E-06 3 120 0.614125 1.70859E-06 0.000125915 0.000134574 4 210 0.522006 1.13906E-05 0.001248655 0.001383229 5 252 0.443705 7.59375E-05 0.008490856 0.009874085 6 210 0.37715 0.00050625 0.040095708 0.049969793 7 120 0.320577 0.003375 0.129833721 0.179803514 8 45 0.272491 0.0225 0.275896657 0.45570017 9 10 0.231617 0.15 0.347425419 0.80312559 10 1 0.196874 1 0.196874404 0.999999994

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