The owner of a fish market determined that the average weight for a catfish is 3.4 pounds with a standard deviation of 0.8 of a pound.A citation catfish should be one of the top 2% in weight.Assuming the weights of catfish are normally distributed,at what weight (in pounds)should the citation designation be established?
A)1.65 pounds
B)5.04 pounds
C)5.42 pounds
D)6.76 pounds

Question

Quizplus · Accepted Answer

To find the weight at which a catfish would be in the top 2% (or the 98th percentile) in a normal distribution, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in the distribution, μ is the mean, and σ is the standard deviation. For the top 2%, the Z-score is approximately 2.05 (from standard Z-tables). Plugging in the values: 2.05 = (X - 3.4) / 0.8, solving for X gives X ≈ 5.04 pounds.

The Owner of a Fish Market Determined That the Average