The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. based on a large number of observations, the distribution of trout weights is normally distributed with a mean of 402.7 grams and a standard deviation 8.8 grams. what is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?

The normal distribution curve for the problem is shown below

We need to standardise the value X=405.5 by using the formula




We now need to find the probability of z=0.32 by reading the z-table

Note that z-table would give the reading to the left of z-score, so if your aim is to work out the area to the right of a z-score, then you'd need to do:



from  the z-table, the reading  gives 0.6255

hence, 


The probability that the mean weight for a sample of 40 trout exceeds 405.5 gram is 0.3475 = 34.75%

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)