Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent:
-The average size of the bass in a lake is 11.4 inches, with a standard deviation of 3.2 inches. Find the probability of catching a bass longer than 17 inches.
A) 4%
B) 8%
C) 5%
D) 96%

Question

Quizplus · Accepted Answer

To find the probability of catching a bass longer than 17 inches, we use the Z-score formula: Z = (X - μ) / σ, where X is the value (17 inches), μ is the mean (11.4 inches), and σ is the standard deviation (3.2 inches). Plugging in the values, we get Z = (17 - 11.4) / 3.2 = 5.6 / 3.2 = 1.75. Looking up the Z-score of 1.75 in the standard normal distribution table or using a calculator, we find that the area to the left of Z = 1.75 is approximately 0.96, meaning 96% of the data falls below 17 inches. Therefore, the probability of catching a bass longer than 17 inches is 1 - 0.96 = 0.04, or 4%.

Assume the Distribution Is Normal