An aptitude test was given to a random sample of 175 applicants for a training p

Question

An aptitude test was given to a random sample of 175 applicants for a training program. The results are shown below where x is the score on a 4 point scale, and f is the frequency of people with this score.

A) use the relative frequencies to find P(x) for x=1 to4 ( in decimal form - 3 decimal places. ) X= 1 2 3 4 F= 17, 53, 58, 47

B)to be accepted into a training program, students must have a score of 3 or higher. what is the probability an applicant selected at random will have this score?

C) To receive a tuition scholarship a student needs a score of 4. what is the probability an applicant selected at random will have such a score?

D) Using calculation from your table:

Compute the expected value of the x distribution

compute the standard deviation of the x distribution

Explanation / Answer

a)

b) P(X >= 3) = P(X = 3) + P(X = 4) = 0.331 + 0.269 = 0.6

c) P(selected student has score 4) = P(X = 4) = 0.269

d) E[X] = x*P(X) = 1*0.097 + 2*0.303 + 3*0.331 + 4*0.269 = 2.772

Var(X) = (x-E[X])2*P(X) = (1-2.772)2*0.097 + (2-2.772)2*0.303 + (3-2.772)2*0.331 + (4-2.772)2*0.269 = 0.9080
Std dev(X) = sqrt(Var(X)) = sqrt(0.9080) = 0.9529

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