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 85 inches and a standard deviation of 10 inches. Directions: Make a sketch of the "empirical rule" for this setting. a) What proportion of frog jumps are less than 75 inches? b) What jump lengths represent the middle 95% of frog jumps? Between and c) What is the probability of observing a random frog jump that is longer than 105 inches?

Answer 1

Given,

X : Jump length

X approximately normally distributed with a : mean of 85 inches and a : standard deviation of 10 inches

proportion of frog jumps are less than 75 inches : From the above picture

P(X<75) = 13.5% + 2.35%+0.15% = 16% i.e 16/100 =0.16

proportion of frog jumps are less than 75 inches =0.16

jump lengths represent the middle 95% of frog jumps

i.e

Between 65 and 105

probability of observing a random frog jump that is longer than 105 inches

P(X>75) = 2.35%+0.15% = 2.5% i.e 0.025

probability of observing a random frog jump that is longer than 105 inches =0.025