Question

At a large university, data were collected on the number of sisters and brothers that each student had. Let the random variable X represent the number of sisters and the random variable Y represent the number of brothers. The distribution of X has mean 1.00 and standard deviation 0.94. The distribution of Y has mean 1.07 and standard deviation 1.04.

What is the mean of the distribution of X+Y?

a) 1.98 b) 2.01 c) 2.04 d) 2.0528 e) 2.07

Answer 1

e) 2.07

Explanation:

When we sum two normally distributed variables.

The mean of the new variable is the sum of the mean of the variables and the variance of the new variable is the sum of the variances of these two variables. The standard deviation is the square root of the variance.

In this problem, we have that:

X has mean 1

Y has mean 1.07

X + Y has mean 1+1.07 = 2.07.

So the correct answer is:

e) 2.07

Answer 2

option E

Explanation:

given,

In distribution of X

mean = 1.00 and Standard deviation = 0.94

In distribution of Y

mean = 1.07 and standard deviation = 1.04

mean of distribution X + Y = ?

now, for large data

the mean of the distribution of X+Y

= mean of x + mean of y

= 1 + 1.07

= 2.07

Hence, the correct answer is option E