1. fish and prawn problem

Dear Sir,
I need help some help with the below problem and would appreciate very much if can offer some help.
thanks
Kingman

Fish and prawns are sold by weight. The masses, in kg, of fish and prawns are modelled as having independent normal distributions with means and standard deviations as shown in the table.

,
Fish : Mean mass = 2.2 , Standard deviation= 0.5
Prawns : Mean mass = 10.5 Standard deviation= 2.1

Fish are sold at $3 per kg and prawns at$5 per kg.

(i) Find the probability that a randomly chosen fish has a selling price exceeding $7. (0.395) (ii) Find the probability of the event that both a randomly chosen fish has a selling price exceeding$7 and a randomly chosen prawn has a selling price exceeding $55. (0.160) (iii) Find the probability that the total selling price of a randomly chosen fish and a randomly chosen prawn is more than$62. (0.392)

(iv) Explain why the answer to part (iii) is greater than the answer to part (ii).

2. (i)
Let X= the price of the fish

$\displaystyle pr(X>7)$

Standardize the normal distribution.

$\displaystyle pr(Z>\frac{7-(2.2)(3)}{(0.5)(3)}$

$\displaystyle pr(Z>0.2667)=\phi (-0.27)\approx 0.3936$

(ii)
For this one you simply have to multiply $\displaystyle pr(X>7)$ (which you found in part (i) by $\displaystyle pr(X>55)$

$\displaystyle pr(X>55)$ is found the same way that $\displaystyle pr(X=7)$ was found for the fish in part (i)

(iii) I'll get to this one if I get a chance

3. Thanks

Thanks very much for the answer but I would appreciate very much if you would
explain to me how you get (2.2)*3 (why this represent the mean) and
(.5)*3 would represent the standard deviation of ...

what formula or reasoning skill you use?

Also can you tell me how to write mathematical symbols on this message window

thanks very much
Kingman

4. (2.2)(3) is the average selling price of the fish.

$\displaystyle \frac {\$2.2}{1kg}*3kg= \frac {(\$2.2)(3kg}{1kg}$

The kg symbols cancel each other out and you're left with:

$\displaystyle \frac{(\$2.2)3}{1}=\$6.6$

(0.5)(3) is the standard deviation of the selling price of the fish.

$\displaystyle \frac{\$0.5}{1kg}*3kg=\frac{(\$0.5)(3kg}{1kg}$

The kg symbols cancel each other out and you're left with:

$\displaystyle \frac{(\$0.5)3}{1}=\$1.5$

http://www.mathhelpforum.com/math-help/latex-help/

Go to this link and read the tutorials on LaTeX to learn how to enter math equations. It takes a bit of getting used to.

5. Thanks

Thanks very much for the help.
In your solution can we write the average price of fish=

($3/1kg)*2.2kg instead of ($2.2/1kg)*3kg

Also can we start working R.V X=mass of chicken—if can then how we continue.
Thanks
Kingman