Complete question :
The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of 3.02 and a standard deviation of .29.Find the probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.
Answer:
0.10868
Step-by-step explanation:
Given that :
Mean (m) = 3.02
Standard deviation (s) = 0.29
Sample size (n) = 20
Probability of 3.10 GPA or higher
P(x ≥ 3.10)
Applying the relation to obtain the standardized score (Z) :
Z = (x - m) / s /√n
Z = (3.10 - 3.02) / 0.29 / √20
Z = 0.08 / 0.0648459
Z = 1.2336940
p(Z ≥ 1.2336) = 0.10868 ( Z probability calculator)
