Statistical Analysis (Normal Distribution)

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Statistical Analysis (Normal Distribution)

Bass: The bass in Clear Lake have weights that are normally distributed with a mean of 2.3 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. 

Bass: The bass in Clear Lake have weights that are normally distributed with a mean of 2.6 pounds and a standard deviation of 0.9 pounds.

(a) Suppose you only want to keep fish that are in the top 20% as far as weight is concerned. What is the minimum weight of a keeper? Round your answer to 2 decimal places. 
 pounds

(b) Suppose you want to mount a fish if it is in the top 0.5% of those in the lake. What is the minimum weight of a bass to be mounted? Round your answer to 2 decimal places. 
 pounds

(c) Determine the weights that delineate the middle 95% of the bass in Clear Lake. Round your answers to 2 decimal places. 
from to pounds

How Laude? Many educational institutions award three levels of Latin honors often based on GPA. These are 
cum laude (with high praise), 
magna cum laude (with great praise), and 
summa cum laude (with highest praise). Requirements vary from school to school. Suppose the GPAs at State College are normally distributed with a mean of 2.9and standard deviation of 0.41.

(a) Suppose State College awards the top 2% of students (based on GPA) with the summa cum laude honor. What GPA gets you this honor? Round your answer to 2 decimal places. 
 GPA or higher

(b) Suppose State College awards the top 10% of students (based on GPA) with the magna cum laude honor. What GPA gets you this honor? Round your answer to 2 decimal places. 
 GPA or higher

(c) Suppose State College awards the top 20% of students (based on GPA) with the cum laude honor. What GPA gets you this honor? Round your answer to 2 decimal places. 
 GPA or higher