Question

Suppose that the probability density function for the length x in feet of some type of fish caught by sport fishermen is given by p(x)=14 if 0≤x≤4, and is zero otherwise. What is the probability that a fish caught by a fisherman is between 0.25 and 2 feet long? 1/4 is less than 0.25 feet long?

Answer 1

Answer:

The probability that a fish caught by a fisherman is between 0.25 feet and 2 feet long is 0.4375.

Step-by-step explanation:

The probability density function or p.d.f. for the length x, in feet, of some type of fish caught by sport fishermen is :

$p(x) = \left \{{{(\frac{1}{4})\ ;\ 0\leq x\leq 4 } \atop{0\ ;\ otherwise} \right.$

The probability that a fish caught by a fisherman is between 0.25 feet and 2 feet long is:

$P(0.25\leq X\leq 2)=\int\limits^{0.25}_{2} {(\frac{1}{4})} \, dx \\=|(\frac{1}{4})x|^{2}_{0.25}\\=(\frac{1}{4})(2-0.25)\\=0.4375$

Thus, the probability that a fish caught by a fisherman is between 0.25 feet and 2 feet long is 0.4375.