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alina1380 [7]
3 years ago
5

Suppose that the probability density function for the length x in feet of some type of fish caught by sport fishermen is given b

y 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?
Mathematics
1 answer:
Firdavs [7]3 years ago
8 0

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 <em>x,</em> 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.

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