Question

(1 point) If xx is a binomial random variable, compute P(x)P(x) for each of the following cases:

(a)  P(x≤3),n=7,p=0.5

P(x≤3)=

(b)  P(x>2),n=6,p=0.8

P(x>2)=

(c)  P(x<4),n=8,p=0.4

P(x<4)=

(d)  P(x≥2),n=7,p=0.3

P(x≥2)=

(1 point) BlueSky Air has the best on-time arrival rate with 80% of its flights arriving on time. A test is conducted by randomly selecting 16 BlueSky Air flights and observing whether they arrive on time.

What is the probability that 2 flights of BlueSky Air arrive late? (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest four decimal places).

Probability (as a proportion)

Answer 1

a)

probability =

P(X<=3)=

∑x=0x     (nCx)px(1−p)(n-x)    =

0.5000

b)

probability =

P(X>=3)=

1-P(X<=2)=

1-∑x=0x-1     (nCx)px(1−p)(n-x)    =

0.9830

c)

probability =

P(X<=3)=

∑x=0x     (nCx)px(1−p)(n-x)    =

0.5941

d)

probability =

P(X>=2)=

1-P(X<=1)=

1-∑x=0x-1     (nCx)px(1−p)(n-x)    =

0.6706

2)

here this is binomial with parameter n=16 and p=1-0.8 =0.2

probability =

P(X=2)=

(nCx)px(1−p)(n-x)    =

0.2111