The mean length of six-year-old rainbow trout in the arolik river in alaska is 481 millimeters with a standard deviation of 41 millimeters. assume these lengths are normally distributed. what proportion of six-year-old rainbow trout are less than 501 millimeters long?

0.688

Step-by-step explanation:

Given: Mean :

Standard deviation :

Sample size :

We assume these lengths are normally distributed.

Then the  formula to calculate the z score is given by :-

For X=501

The p-value of z =

Now, the probability of the newborns weighed between 1492 grams and 4976 grams is given by :-

Hence, The proportion of six-year-old rainbow trout are less than 501 millimeters long = 0.688

The profit is maximum when x = 40.

Step-by-step explanation:

Cost function, C = 40 x + 300

Revenue function, R = 80 x - 0.5 x^2

The profit function is

So, the profit is maximum when x = 40 .