The Fish Commission states that the lengths of all fish in Spring Run are normally distributed, with mean 18 cm and standard deviation 5 cm. What is the probability that a fish caught in Spring Run will be between 18 and 25.5 cm long? Round your answer to four decimal places.
A)0.9332
B)0.4332
C)0.5668
D)0.0668
E)0.8664

Question

The Fish Commission states that the lengths of all fish in Spring Run are normally distributed, with mean 18 cm and standard deviation 5 cm. What is the probability that a fish caught in Spring Run will be between 18 and 25.5 cm long? Round your answer to four decimal places. ​
A)0.9332
B)0.4332
C)0.5668
D)0.0668
E)0.8664

Quizplus · Accepted Answer

To find the probability that a fish caught in Spring Run will be between 18 and 25.5 cm long, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For X = 25.5, Z = (25.5 - 18) / 5 = 1.5. Using the Z-table, the probability of Z being less than 1.5 is approximately 0.9332. Since the probability of a fish being longer than the mean (18 cm) is 0.5 (because of the symmetry of the normal distribution), the probability of a fish being between 18 and 25.5 cm is 0.9332 - 0.5 = 0.4332.

The Fish Commission States That the Lengths of All Fish