The z-score associated with 14.3 is 0.84. 0.2995 of the population is between 12.2 and 14.3. 0.1894 of the population is less than 10.0.
The formula for a z-score is
z=(X-μ)/σ
With our data, we have:
z=(14.3-12.2)/2.5=0.84
The z-score associated with the mean is 0.5. To find the proportion of the population between the mean and 14.3, subtract 0.7995 (the proportion of population below the z-score of 0.84, using http://www.z-table.com) and 0.5:
0.7995 - 0.5 = 0.2995.
The z-score for 10.0 is
(10.0-12.2)/2.5 = -0.88. The proportion of the population less than this is 0.1894.
The total number of fish bought was 320. And you know she bought two types of fish. The best way to solve this is guess and check. It would be the fastest. So she bought 7 times as many trigger-fish as parrot fish that means the number of trigger-fish bought was 7p. This means 320 = 7p +p. So all you do is take educated guesses for the number of parrot fish and check if it is right. So if she bought 50 parrot fish. 7(50) + 50 = 400. Close but a bit high. Lets keep guessing. 7(35) + 35 = 245. So now we know the answer is between 50 and 35. So lets try 40. 7(40) + 40 =320. That works so we know she bought 40 parrot fish and 280 trigger-fish.
4>-3
-2>-5
1=1
They want to make sure you understand inequalities and know how to use the inequality signs.
