Pregunta
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
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
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.
Solución
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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.
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