Suppose that height Y and arm span X for U. S. women, both measured in cm, are normally distributed with means E(Yi) = 168, E(Xi) = 165, variances var(Yi) = 21, var(Xi) = 28, and covariance cov(Xi, Yi) = 20 for measurements on the same individual. For the purpose of this question, the variables are jointly normally distributed, and the values are independent for distinct individuals.
Part a: The correlation between height and arm span is .
Part b: The ‘albatross index’ is the difference Di = Xi − Yi between arm span and height. The mean of D is E(Di) = .
The standard deviation is sd(Di) =
.
Part c: Find the following probabilities for one individual: P(Di >9)= ;
P(Xi >Yi)= ;
P (Xi + Yi > 330) =
Part d: Consider now two specific unrelated individuals named i and j respectively. Compute the following probabilities:
P (Xi − Xj > 10) = ; P (Xi + Xj < 320) = ; P(|Xi −Yi|<10)= ; P (|Xi − Yj | < 10) = .

Part a

0.825

Part b

17.12

Part c

(I) 0.4325

(ii) 0.659

(iii) 2.5E-4

Part d

(I) 0.0902

(ii) 0.902

(iii)0.146

(iv) 0.1265

Step-by-step explanation: Check attachment

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.