Question

1. Refer to the table below “Undergraduate Grade Record by Student Characteristic” to answer this question

a) What is the probability that a graduating senior has grades mostly consisting of B’s or higher? Show and justify your calculation

b) What is the probability that a student selected at random has grades mostly B’s given they are in the age range 19-23?

c) Suppose that 65% of the students are in the age range 19-23. What is the probability that a student selected at random is both in this age range and has grades that are B’s and C’s. Justify your calculation

d) Write down a probability distribution from this chart – state the random variable, it’s possible outcomes and give the probability associated with each outcome

Student characteristic			C's and D's or lower	B's and C's	Mostly B's	A's and B's	Mostly A's
Gender	Men		38.8%	16.6%	22.6%	9.6%	12.4%
	Women		29.4%	16.2%	26.2%	12.0%	16.2%
Class Level	Graduating Senior		15.8%	21.9%	34.5%	14.7%	13.0%
	All othe class levels		35.4%	15.8%	23.6%	10.5%	14.7%
Age	18 or younger		42.6%	14.7%	23.4%	9.4%	10.0%
	19-23		38.1%	19.0%	25.1%	9.4%	8.3%
	24-29		33.3%	16.9%	24.7%	10.3%	14.9%
	30-39		23.1%	13.2%	25.9%	14.8%	23.0%
	40 and older		20.1%	10.1%	22.0%	14.8%	33.0%

Answer 1

a.

The probability that a graduating senior has grades mostly consisting of B’s or higher:

P = 34.5 + 14.7 + 13 = 62.2% = 0.622

b.

The probability that a student selected at random has grades mostly B’s given they are in the age range 19-23 is 25.1% = 0.251

c.

Let event A = the students are in the age range 19-23 = 0.65

Let event B = has grades that are B’s and C’s = 0.19

Hence P(A and B) = P(A) * P(B) = 0.65 * 0.19 = 0.1235

d.

Let random variable X =. grades of graduating seniors

Possible values of X are C's and D's or lower, B's and C's , Mostly B's, A's and B's and Mostly A's.

Probability distribution of X is

X	C's and D's or lower	B's and C's	Mostly B's	A's and B's	Mostly A's
Prob P(X)	0.158	0.219	0.345	0.147	0.13