Suppose that the probability that a person will remember between 100a% and 100b% of material learned in an experiment is where x represents the proportion remembered. Determine from the figure below, the probability that a randomly chosen individual will recall between 50% and 75% of the material? Express your answer as a percent rounded to three decimal places.
A) 19.900%
B) 12.500%
C) 11.000%
D) 35.300%
E) 106.600%

Question

Suppose that the probability that a person will remember between 100a% and 100b% of material learned in an experiment is  where x represents the proportion remembered. Determine from the figure below, the probability that a randomly chosen individual will recall between 50% and 75% of the material? Express your answer as a percent rounded to three decimal places. 
A) 19.900% 
B) 12.500% 
C) 11.000% 
D) 35.300% 
E) 106.600%

Quizplus · Accepted Answer

From the given information, we have the probability that a person will remember between 100a% and 100b% of material learned as 11eaa595_656d_3f9f_a696_75f2a3a505b7_TB4584_11_TB4584_11, where x represents the proportion remembered.

To find the probability that a person recalls between 50% and 75% of the material, we need to find the probability of x being between 0.5 and 0.75.

So, we need to evaluate the given probability function at x = 0.5 and x = 0.75 and find the difference between these values to get the required probability.

P(0.5 ≤ x ≤ 0.75) = P(x ≤ 0.75) - P(x ≤ 0.5)

Substituting the values of x, we get:

P(0.5 ≤ x ≤ 0.75) = 11(0.75)^9 - 11(0.5)^9 = 0.352997

Therefore, the probability that a randomly chosen individual will recall between 50% and 75% of the material is 0.352997 or 35.300% (rounded to three decimal places).

Hence, the answer is D.

Suppose That the Probability That a Person Will Remember Between