Question

a) If you have 4 cousins, what is the probability that 3 or more are male? (Assume male and female are equally likely).

b) In a normal distribution, what percent of scores are in T-score of 51 or higher?

c) If you roll two 6-sided dice, what percent of the time do both dice show numbers from 4 to 6?

d) In an elementary school, the correlation between age and height for all students in the school is _________ than the same correlation for only the fourth graders.

Answer 1

Result:

a) If you have 4 cousins, what is the probability that 3 or more are male? (Assume male and female are equally likely).

n=4, p=0.5, binomial distribution used.

Binomial Probabilities Table
	X	P(X)
	0	0.0625
	1	0.2500
	2	0.3750
	3	0.2500
	4	0.0625

P( x ≥3) = P( x=3)+P( x=4) =0.2500+0.0325

=0.2825

b) In a normal distribution, what percent of scores are in T-score of 51 or higher?

T score having mean 50 and standard deviation of 10

Z value for 51, z =(51-50)/10 = 0.1

P( T >51) = P( z > 0.1) =0.4602

The required percentage =46.02%

c) If you roll two 6-sided dice, what percent of the time do both dice show numbers from 4 to 6?

The sample space:

(1,1)	(1,2)	(1,3)	(1,4)	(1,5)	(1,6)
(2,1)	(2,2)	(2,3)	(2,4)	(2,5)	(2,6)
(3,1)	(3,2)	(3,3)	(3,4)	(3,5)	(3,6)
(4,1)	(4,2)	(4,3)	(4,4)	(4,5)	(4,6)
(5,1)	(5,2)	(5,3)	(5,4)	(5,5)	(5,6)
(6,1)	(6,2)	(6,3)	(6,4)	(6,5)	(6,6)

Number of times both dice show numbers from 4 to 6 = 9

percent of the time do both dice show numbers from 4 to 6 = (9/36)*100 = 25%

d) In an elementary school, the correlation between age and height for all students in the school is larger than the same correlation for only the fourth graders.

(If you restrict the range of the variables, that usually reduces the correlation)