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Vedmedyk [2.9K]
2 years ago
15

Question 12 The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of and

a standard deviation of . Find the probability that the mean GPA of a random sample of students selected from this university is or higher.
Mathematics
1 answer:
andreev551 [17]2 years ago
8 0

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)

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