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Question 23 Not yet answered Points out of 4.00 lag question There are 5 radar stations and the probability of a single radar station detecting an enemy plane is 0.75. What is the probability of 3 stations detecting an enemy plane? Round your answer to nearest hundredth. Select one: a. 0.26 b. 0.06 O C. 0.07 o d. 0.03 O e. 0.75 Next page Previous page 4 Week 3 Reflection Assignment Jump to...

Answer 1

Question 23 :

n = number of radar stations = 5

p = P( Radar station detecting an enemy plane) = 0.75.

Let X denotes number of radar stations detecting an enemy plane.

X takes values 0,1, ......,5.

The probability distribution of random variable X as binomial with n =5 and p = 0.75.

i.e. X ~ Bin ( n = 5, p = 0.75)

Required Probability = P ( X=3)

= ⁵C₃ * (0.75)³ * ( 0.25) ²

= 0.264

Correct Answer - a. 0.26

Question 20 :

n = number of radar stations used = 4

p = P( Radar station detecting an enemy plane) = 0.85.

Let Y denotes number of radar stations detecting an enemy plane.

Y takes values 0,1, ......,4.

i.e. Y ~ Bin ( n = 4 , p = 0.85)

If Y ~ Bin (n, p)

then E(Y) = mean = np = 4 *0.85 = 3.4

and Variance = n*p*(1-p) =4*0.85*0.15 = 0.51

Standard deviation = sqrt(Variance) = sqrt(0.51)

= 0.714

Correct Answer - e. 0.71