Question 5 A particle executes a simple unrestricted random walk on the line: a

Question

Question 5 A particle executes a simple unrestricted random walk on the line: a step to the right of length 1 occurs with probability 0.54 and a step to the left of length 1 occurs with probability 0.46. Initially the particle is at the origin. Select the option that gives an approximate value for the probability that the particle will be less than 6 units from the origin after 100 steps, calculated using an appropriate continuity correction. Select one: O 0.715 O 0.285 O 0.660o O 0.340 O 0.607 O 0.393

Explanation / Answer

p = 0.54

n = 100

np = 54 , sqrt(npq) = sqrt(100*0.54*0.46) = 4.98397

P(47 < X< 53)

=P(47.5 < X< 52.5)

= P ( 1.3<Z<0.3 )=0.2853

option B) is correct

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