Question

Q3 – Normal Distribution (10 pts).

suppose we have 10 students with the following grades: 34, 67, 45, 87, 75, 49, 68, 59, 70, 74

1. Find sum, average, SD, Z-score
2. what is the probability of a student to get 71
3. what is the probability to get a grade between 60 and 70
4. what is the probability to get a grade > 77

Answer 1

	Grades
	34
	67
	45
	87
	75
	49
	68
	59
	70
	74	Excel formulas
SUM	628	SUM(B2:B11)
AVERAGE	62.8	AVERAGE(B2:B11)
SD	16.0125	STDEV(B2:B11)

n = 10

a)the probability of a student to get 71

Z = (X bar - μ) / (σ / SQRT(n))

Z = (71 - 62.8) / (16.0125/SQRT(10)) = 1.6194

P(X = 71) = P(Z = 1.6194) = 0.9473

b)the probability to get a grade between 60 and 70

P(60 < X < 70) = P((60 - 62.8) / (16.0125/SQRT(10)) < Z < (70 - 62.8) / (16.0125/SQRT(10)))

= P(-0.5531 < Z < 1.4219) = P(Z < 1.4219) - P(Z < -0.5531) = 0.9225 - 0.2901

P(60 < X < 70) = 0.6324

c)the probability to get a grade > 77

P(X > 77) = P(Z > (77 - 62.8) / (16.0125/SQRT(10))) = P(Z > 2.8043)

P(X > 77) = 0.0025