Answer all questions neatly! 4. The Hulliaa learning model asserts that the prob

Question

Answer all questions neatly!

4. The Hulliaa learning model asserts that the probability p of mastering a task after t learning trails is approximated by P(t) = 1 e-kt - where k is a constant that depends on the task to be learned. Suppose that a new dance is being taught on Dancing with the Stars. For this particular dance, the constant 0.31 a) What is the probability of mastering the dance's steps in 1 trial? (3 decimal places) b) What is the probability of mastering the dance's steps in 5 trials? (3 decimal places) c) Find the rate of change, P'(t). P'(t) = d) If you were on Dancing With the Stars, how many times would you have to repcat the dance before you had a probability of .952 (95.2% chance) of having mastered it? (nearest whole number)

Explanation / Answer

a) probability of mastering dance's step in 1 trail=P(t=1)=1-e-0.31*1 =1-0.733 =0.267

b)probability of mastering dance's step in 5 trail=1-e-0.31*5 =1-0.212 =0.788

c)rate of change P'(t) =(d/dt)*P(t) =(d/dt)*(1-e-0.31t) =0.31*e-0.31t

d)

for let number of steps required are t

hence P(t)=1-e-0.31t >=0.952

e-0.31t <=1-0.952

e-0.31t <=0.048

taking log on both sides and solving

t>=9.795

hence minimum time it is required =10

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