Question

A government's department of transportation reported that in 2009, airline Aled al domestic airlines in on-time arrivals for domestic flights, with a rate of 84%. Complete parts a through e below. What is the probability that in the next six flights, exactly four flights will be on time? The probability is (Round to four decimal places as needed) b. What is the probability that in the next six flights, two or fewer will be on time? The probability is (Round to four decimal places as needed) e. What is the probability that in the next six flights, at least four flights will be on time? The probability is (Round to four decimal places as needed) d. What are the men and Mandard deviation for this distribution? The mean of the number of on time arrivals in (Type an integer or a decimal) The standard deviation of the number of on-time arrival is (Round to four decimal places as needed) . Construct a histogram for this distribution. Choose the correct graph below ОА Oc Binomia Bom Pro Binomia Distribution 05 Number one Number of time Number of time was

Answer 1

Probability that the all domestic airlines will be in time = 0.84

this is a binomial distribution.

a) Probability that in the next 6 flights, exactly 4 will be on time,

P(X = 4

(0) *0.844 * (1 – 0.84)6-4 = 0.1912

b) Probability that in the next 6 flights, two or fewer will be on time,

$\small P(X \leq 2)$

  $\small =P(X=0)+P(X=1)+P(X=2)$

$\small = \binom{6}{0}*0.84^{0}*(1-0.84)^{6-0} +\binom{6}{0}*0.84^{1}*(1-0.84)^{6-1}+\binom{6}{2}*0.84^{2}*(1-0.84)^{6-2}$

= 0.0075

c) Probability that in the next 6 flights, at least 4 flights will be on time,

  $\small P(X \geq 4)$

$\small =P(X=4)+P(X=5)+P(X=6)$

$\small = \binom{6}{4}*0.84^{4}*(1-0.84)^{6-4} +\binom{6}{5}*0.84^{5}*(1-0.84)^{6-5}+\binom{6}{6}*0.84^{6}*(1-0.84)^{6-6}$

= 0.9440

d) Mean and standard deviation of the dstribution,

Mean = n*p = 6*0.84 = 5.04

Variance = n*p*(1-p) = 6*0.84*(1-0.84) = 0.8064

Standard deviation = $\tiny \sqrt{0.8064}$ = 0.8980

e) Histogram of the distribution,

  

Binomial Probability Distribution 0.45 0.4 0.35 0.3 0.25 0.2 PIX) 0.15 0.1 0.05 0 0 1 2 3 4 5 6

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