Question

The average length of crocodiles in a swamp is 10.5 feet. If the lengths are normally distributed with a standard deviation of 1.3 feet, find the probability that a crocodile is more than 10 feet long. In addition to the answer, please write out your steps and thoughts that led you to your answer

Answer 1

This is a normal distribution question with

\\Mean (\mu)= 10.5
\\Standard\;Deviation (\sigma)= 1.3
\\Since\; we\; know\; that
\\z_{ score } = \frac{x-\mu}{\sigma}

P(x > 10.0)=?

The z-score at x = 10.0 is,

z = \frac{10.0-10.5}{1.3}

z = -0.3846

This implies that

P(x > 10.0) = P(z > -0.3846) = 1 - P(z < -0.3846) = 1 - 0.35026689706197084

PS: you have to refer z score table to find the final probabilities.

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