Question

11.

Suppose we have a box model representing a die: [1,2,3,4,5,6] with a mean of μ=3.5 and a standard deviation of σ=1.708. If we do 88 rolls of the die what is the probability that the sum will be less than 300?

Question 11 options:

	A) 0.3085
	B) -0.50
	C) 0
	D) 0.6915
	E) 0.50

3.

Suppose we have the following box representing our population [0, 1, 1, 2, 3, 5] with μ=2.0 and σ=1.79. If we sample or draw from this population 35 times, what is the probability that the sum exceeds 85 is ______.

Question 3 options:

	A) 92.22%
	B) 14.26%
	C) 15.58%
	D) 7.78%
	E) 29.54%

Answer 1

die: [1,2,3,4,5,6] with a mean of =3.5 and a standard deviation of =1.708

If we do 88 rolls of the die, then the sum will be a normal distribution with mean = 88 = 88 x 3.5 = 308

And standard deviation =

Probability that the sum will be less than 300 = P(Sum < 300)

Z-score for 300 = (300-308)/16.02 = -0.5

From standard normal tables, P(Z<-0.5) = 0.3085

Ans : A) 0.3085

Suppose we have the following box representing our population [0, 1, 1, 2, 3, 5] with =2.0 and =1.79

sample or draw from this population 35 times, the sum will be a normal distribution with mean: 35 = 35x2.0=70

and standard deviation =

Probability that the sum exceeds 85 = P(Sum>85) = 1-P(Sum85)

Z-score for 85 = (85-70)/10.59 = 1.42

From standard normal tables, P(Z1.42) = 0.9222

P(Sum85) = P(Z1.42) = 0.9222

P(Sum>85) = 1-P(Sum85) = 1-0.9222=0.0778

Probability that the sum exceeds 85 = 0.0778 =7.78%

Ans : D) 7.78%