Question

At a certain college, 50% of all students take advantage of free tutoring services. A sample of 36 students is selected. What is the probability that the proportion of students who take advantage of free tutoring services in the sample is between 0.475 and 0.580?

Write only a number as your answer. Round to 4 decimal places for example 0.3748 ). Do not write as a percentage .

Answer 1

We know that the sample proportion is distributed as:

P(1 – P))~ N(0.5, 0.5(1 – 0.5)) ~ N(0.5, p~ N(P, 1 144 n 36

Required probability =

0.580 – 0.5 0.475 – 0.5 P(0.475 <p < 0.580) = PC- < Z < 1 144 = P(-0.30<Z < 0.96) = P(Z < 0.96) – P(Z <-0.30) = P(Z < 0.96) - P(Z > 0.30) = P(Z < 0.96) – [1 – P(Z <0.30) = 0.83147 – [1 – 0.61791] = 0.44938 0.4494