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 2.5 pounds and a standard deviation of 0.8 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 weight = 2.5 pounds

standard deviation = 0.8 pounds

(a) Here if the weight of random bass is x pounds

then,

Pr(x < 1 pound) = NORM (x < 1 pound ; 2.5 pound ; 0.8 pound)

Z = (1- 2.5)/0.8 = -1.875

Pr(x < 1 pound) = NORM (x < 1 pound ; 2.5 pound ; 0.8 pound) = Pr(Z < -1.875) = 0.0304

(b) Pr(x > 3 pound) = 1 - NORM (x < 3 pound ; 2.5 pound ; 0.8 pound)

Z = (3 - 2.5)/0.8 = 0.625

Pr(x > 3 pound) = 1 - NORM (x < 3 pound ; 2.5 pound ; 0.8 pound) = 1 - Pr(Z < 0.625)  

= 1 - 0.7340 = 0.2660

(c) Pr(1 pound < x < 3 pound) = Pr(x < 3 pound) - Pr(x < 1 pound) = 0.7340 - 0.0304 = 0.7036

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