When you roll 2 four-sided dice and add the results you can get any integer from

Question

When you roll 2 four-sided dice and add the results you can get any integer from 2 to 8. The probability distribution for X
X
, the sum obtained when rolling a pair of four-sided dice, is shown.

X = sum   2   3   4   5   6   7   8
P(X)   0.0625   0.125   0.1875   0.25   0.1875   0.125   0.0625
This distribution has a mean (expected value) of 5 and a standard deviation of 1.58.

A. What proportion of this probability distribution is within one standard deviation of the mean? .

Proportion =

B. What proportion of this probability distribution is within two standard deviations of the mean?

Proportion =

C. What shape best describes this distribution? Enter 1 for skewed left, enter 2 for skewed right, enter 3 for uniform, and enter 4 for bell shaped.

Shape is

Explanation / Answer

A) Within 1 standard deviation of mean implies that the value is between 5-1.58 and 5+1.58, i.e, 3.42 and 6.58

P(within 1 standard deviation) = 0.1875 + 0.25 + 0.1875 = 0.625

b) Within 2 standard deviations means, within 5-2x1.58 and 5+2x1.58

i.e, within 1.84 and 8.16 = 1

C) 4 - bell shaped

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.