A random sample of 20 students is selected. What is the probability that the sample
proportion exceeds 75%, i.e., more than 15 students (out of 20 selected) will agree that
that the course is interesting? You may leave your answer as, for example, 1 − 0.88. (As a
standard error use 0.8. Also, in your calculations instead of 1/8 = 0.125 you may use 0.13).
Solution: given by professor
1. Sampling distribution of the sample proportion.
P(p >b 0.75) = P (Z >( 0.75 − 0.7 )/0.8)= P (Z > 0.25) = 1 − PZ ≤ 0.25= 1 − 0.5987 = 0.4013.
2. Normal approximation to a Binomial distribution.
Let X be the number of students in the sample who find the course interesting, then
the mean of X is 14.
P(X ≥ 15) = P ((Z ≥ 14.5 − 14 )/0.8) = P (Z ≥ 0.65 )= 1 − P( Z < 0.65) = 1 − 0.7422 = 0.2578
proportion exceeds 75%, i.e., more than 15 students (out of 20 selected) will agree that
that the course is interesting? You may leave your answer as, for example, 1 − 0.88. (As a
standard error use 0.8. Also, in your calculations instead of 1/8 = 0.125 you may use 0.13).
Solution: given by professor
1. Sampling distribution of the sample proportion.
P(p >b 0.75) = P (Z >( 0.75 − 0.7 )/0.8)= P (Z > 0.25) = 1 − PZ ≤ 0.25= 1 − 0.5987 = 0.4013.
2. Normal approximation to a Binomial distribution.
Let X be the number of students in the sample who find the course interesting, then
the mean of X is 14.
P(X ≥ 15) = P ((Z ≥ 14.5 − 14 )/0.8) = P (Z ≥ 0.65 )= 1 − P( Z < 0.65) = 1 − 0.7422 = 0.2578
