Question

10. The grade distribution of a Basic English course in a high school (total 3500 students) is normally distributed with its mean, 3.2 and standard deviation, 0.61. 1) If a student is randomly selected, find the probability that the student’s score is higher than 3.0?2) If you collect a sample of 30 students, what is the probability that the sample mean is less than 3.0?

Answer 1

Solution :

1)

P(x > 3.0) = 1 - P(x < 3.0)

= 1 - P[(x - ) / < (3.0 - 3.2) / 0.61)

= 1 - P(z < -0.3279)

= 1 - 0.3715

= 0.6285

Probability = 0.6285

2)

= / n = 0.61/ 30 = 0.1114

P( < 3.0) = P(( - ) / < (3.0 - 3.2) / 0.1114)

= P(z < -1.7953)

= 0.0363

Probability = 0.0363