Bass: The bass in Clear Lake have weights that are normally distributed with a m

Question

Bass: The bass in Clear Lake have weights that are normally distributed with a mean of 2.1 pounds and a standard deviation of 0.6 pounds.

(a) If you catch one random bass from Clear Lake, find the probability that it weighs less than 1 pound? Round your answer to 4 decimal places.


(b) If you catch one random bass from Clear Lake, find the probability that it weighs more than 3 pounds? Round your answer to 4 decimal places.


(c) If you catch one random bass from Clear Lake, find the probability that it weighs between 1 and 3 pounds? Round your answer to 4 decimal places.

Explanation / Answer

Mean ( u ) =2.1
Standard Deviation ( sd )=0.6
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a.
P(X < 1) = (1-2.1)/0.6
= -1.1/0.6= -1.8333
= P ( Z <-1.8333) From Standard Normal Table
= 0.0334
                  
b.
P(X > 3) = (3-2.1)/0.6
= 0.9/0.6 = 1.5
= P ( Z >1.5) From Standard Normal Table
= 0.0668                  

c.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 1) = (1-2.1)/0.6
= -1.1/0.6 = -1.8333
= P ( Z <-1.8333) From Standard Normal Table
= 0.03338
P(X < 3) = (3-2.1)/0.6
= 0.9/0.6 = 1.5
= P ( Z <1.5) From Standard Normal Table
= 0.93319
P(1 < X < 3) = 0.93319-0.03338 = 0.8998                  

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