Score on last try: 0.5 of 1 pts. See Details for more. S Get a similar question You can retry this question below A researcher studying frogs is investigating the distance that a certain species of frog can jump. The jump lengths appear to be approximately normally distributed with a mean of 90 inches and a standz deviation of 8 inches. Directions: Use the "empirical rule" (68-95-99.7) for this setting. a) What proportion of frog jumps are less than 74 inches?

To determine the proportion of frog jumps less than 74 inches, we first need to find how many standard deviations away from the mean this value is. The mean jump length is 90 inches, and the standard deviation is 8 inches. The difference between the mean and 74 inches is 90 - 74 = 16 inches. Dividing this by the standard deviation gives us 16 / 8 = 2. This means 74 inches is 2 standard deviations below the mean. According to the empirical rule (68-95-99.7), about 95% of the data falls within 2 standard deviations of the mean in both directions. Consequently, 2.5% of the frog jumps will be below 2 standard deviations (74 inches), which means that the proportion of frog jumps less than 74 inches is 0.025 or 2.5%. In simpler terms, if you lined up a bunch of frogs in a jumping competition, there's a very small chance that you would see a leap shorter than 74 inches — only about 2.5 out of every 100 jumps! So keep your eyes peeled for those impressive jumpers, because most of them will be leaping much farther!