Question

The final exam grade of a mathematics class has a normal distribution with mean of 81 and standard deviation of 6.6. If a random sample of 40 students selected from this class, then what is the probability that the average final exam grade of this sample is between 77 and 82? Answer: (keep 4 decimal places)

Answer 1

Solution :

Given that,

mean = = 81

standard deviation = = 6.6

n = 40

=81

₌ / n = 6.6 40 = 1.0435

P (77 < < 82)

P ( 77 - 81 / 1.0435) < ( - /  ) < ( 82 - 81 / 1.0435)

P ( - 4 / 1.0435 < z < 1 / 1.0435 )

P (-3.83 < z < 0.96)

P ( z < - 0.259 ) - P ( z < -3.83)

Using z table

= 0.8315 - 0.0001

= 0.8314

Probability = 0.8314