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
gugj
To answer these questions, we will use the properties of the normal distribution and the Z-score. The formula for calculating the Z-score is:
Z = (X - μ) / σ
Where:
X is the value we are interested in,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.
Once we have calculated the Z-score, we can use the Z-table or a statistical calculator to find the corresponding probability.
Now let's solve each question step by step.
Question (a):
To find the probability that a random bass weighs less than 1 pound, we need to calculate the Z-score for 1 pound using the given mean and standard deviation.
Z = (1 - 2.3) / 0.6
Calculate this value to find the Z-score for 1 pound.
Once you have the Z-score, you can use the Z-table or a statistical calculator to find the corresponding probability.
Question (b):
To find the probability that a random bass weighs more than 3 pounds, we need to calculate the Z-score for 3 pounds using the given mean and standard deviation.
Z = (3 - 2.3) / 0.6
Calculate this value to find the Z-score for 3 pounds.
Once you have the Z-score, you can use the Z-table or a statistical calculator to find the corresponding probability.
Question (c):
To find the probability that a random bass weighs between 1 and 3 pounds, we need to calculate the Z-scores for both 1 and 3 pounds using the given mean and standard deviation.
Calculate the Z-score for 1 pound and the Z-score for 3 pounds.
Once you have the Z-scores, you can use the Z-table or a statistical calculator to find the corresponding probabilities for each Z-score. Then subtract the probability for 1 pound from the probability for 3 pounds to get the probability between 1 and 3 pounds.
Question (d):
To find the minimum weight of a bass to be considered a keeper (top 20%), we need to find the Z-score that corresponds to the top 20% of the distribution.
Find the Z-score from the Z-table or using a statistical calculator for the top 20% (which is equivalent to 1 - 0.2 = 0.8).
Once you have the Z-score, you can use it to find the corresponding weight using the formula:
Weight = Z * σ + μ
Question (e):
To find the minimum weight of a bass to be mounted (top 0.5%), we need to find the Z-score that corresponds to the top 0.5% of the distribution.
Find the Z-score from the Z-table or using a statistical calculator for the top 0.5% (which is equivalent to 1 - 0.005 = 0.995).
Once you have the Z-score, you can use it to find the corresponding weight using the same formula as in question (d).
Question (f):
To determine the weights that delineate the middle 95% of the bass in Clear Lake, we need to find the Z-scores that correspond to the middle 95% (which is equivalent to (1 - 0.95) / 2 and 1 - (1 - 0.95) / 2).
Find the Z-scores from the Z-table or using a statistical calculator for both of these probabilities.
Once you have the Z-scores, you can use them to find the corresponding weights using the formula mentioned earlier.
Now you have the step-by-step approach to solve these questions. You can apply these steps to calculate the answers to each question.
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, I will give you a start.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
This should help you with several of the problems.