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Answer:
The probability that a Red Drum fish caught on the Texas coast can be brought home for dinner is 0.1508.
Step-by-step explanation:
Consider the provided information.
The mean length of the Red Drum fish captured by the scientists is 15.4 inches, with a standard deviation of 4.5 inches.
The Z score formula is: [tex]Z=\frac{x-\mu}{\sigma}[/tex]
From the above information.
σ=4.5, x=15.4
A Current Texas Parks and Wildlife regulations (laws) only allow fishermen to keep Red Drum fish that are between 20 and 28 inches long.
Therefore,
[tex]P(20<X<28)=P(\frac{(20-15.4)}{4.5}<Z<\frac{(28-15.4)}{4.5})[/tex]
[tex]P(20<X<28)=P(\frac{4.6}{4.5}<Z<\frac{12.6}{4.5})[/tex][tex]P(20<X<28)=0.8467-0.9974 =0.1508[/tex]
Hence, the probability that a Red Drum fish caught on the Texas coast can be brought home for dinner is 0.1508.
Answer:
0.15 is the probability that a Red Drum fish caught on the Texas coast can be brought home for dinner. Â
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 15.4 inches
Standard Deviation, σ = 4.5 inches
We are given that the distribution of lengths of Red Drum fish is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(Red Drum fish that are between 20 and 28 inches long)
[tex]P(20 \leq x \leq 28) = P(\displaystyle\frac{20 -15.4}{4.5} \leq z \leq \displaystyle\frac{28-15.4}{4.5}) = P(1.0222 \leq z \leq 2.8)\\\\= P(z \leq 2.8) - P(z < 1.0222)\\= 0.997 - 0.847 = 0.15 = 15\%[/tex]
[tex]P(20 \leq x \leq 28) = 15\%[/tex]
0.15 is the probability that a Red Drum fish caught on the Texas coast can be brought home for dinner.
