You have observed that the average size of a particular goldfish is 1.5 inches long. The standard deviation of the size of the goldfish is 0.25 inches. What is the size of a goldfish such that 90 percent of the goldfish are smaller from such size? Assume a normal distribution for the size of goldfish. Round your final answer to two decimal places.
A) 1.01 inches
B) 1.09 inches
C) 1.91 inches
D) 1.99 inches

Question

Quizplus · Accepted Answer

To find the size of a goldfish such that 90% are smaller, we look for the z-score corresponding to the 90th percentile in a standard normal distribution, which is approximately 1.28. Using the formula for converting a z-score to a raw score in a normal distribution, $X = \mu + Z\sigma$, where $\mu$ is the mean (1.5 inches), $\sigma$ is the standard deviation (0.25 inches), and $Z$ is the z-score (1.28), we calculate $X = 1.5 + (1.28)(0.25) = 1.5 + 0.32 = 1.82$. Rounding to two decimal places, the closest answer provided is 1.91 inches.

You Have Observed That the Average Size of a Particular