Question
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 standard
deviation of 8 inches.
Directions: Use the “empirical rule”
a) What proportion of frog jumps are less than 74 inches?
b) What jump lengths represent the middle
106
c) What is the probability of observing a random frog jump that is longer than 98 inches? 16
Submit Question
jump lengths appear to be approximately normally distributed with a mean of 90 inches and a standard
deviation of 8 inches.
Directions: Use the “empirical rule”
a) What proportion of frog jumps are less than 74 inches?
b) What jump lengths represent the middle
106
c) What is the probability of observing a random frog jump that is longer than 98 inches? 16
Submit Question
Ask by Cook Ray. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a) Approximately 2.5% of frog jumps are less than 74 inches.
b) The middle 95% of frog jumps are between 74 inches and 106 inches.
c) There is a 16% probability of observing a frog jump longer than 98 inches.
Solution
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The Deep Dive
If we apply the empirical rule, we know that about 68% of the jumps fall within one standard deviation of the mean (from 82 to 98 inches) and about 95% fall within two standard deviations (from 74 to 106 inches). Therefore, approximately 16% of jumps are less than 74 inches, since this is the lower tail of the two standard deviations.
To find the probability of observing a jump longer than 98 inches, we can look at the upper tail. Since 68% of jumps fall between 82 and 98 inches, we can deduce that another 16% of jumps are longer than 98 inches, as they also fall within the remaining area of the normal distribution curve.
