Question

The weight of a medium sized orange selected at random froma large bin of orangesat the local supermarket is a random variable with mean=12 ounces and standard deviation=1.2 ounces. Suppose we independently pick two oranges at random from the bin. The difference in the weights of the two oranges selected(the weight of the first orange minus the weight of the second orange)is a random variable with what mean and standard deviation approximately?(2-decimal places)
x=first orange weight
y=second orange weight

Answer 1

Answer:

Step-by-step explanation:

Here Z=X-Y is the random variable denoting the difference in the weight between two oranges selected

X,Y~N(12, 1.2) as number of oranges was large and the oranges were picked randomly

Now we know,

$A\sim N(\mu_{1} ,\sigma _{1}^{2}) \and \ B\sim N(\mu _{2},\sigma _{2}^{2}) \ then \\ cA+dB\simN(\ cu_{1}+du _{2},c^{2}\sigma _{1}^{2}+d^{2}\sigma _{2}^{2})$

Hence Z~N(0, 1.69706)

mean=0

Standard Deviation =1.70 (approximated )