Let xx represent the full height of certain species of tree. Assume that xx is normally distributed with a mean of 140.3 feet and a standard deviation of 6.5 feet. Find the probability that the full height of a randomly selected tree is less than 146.8 feet.

Let xx represent the full height of certain species of tree. Assume that xx is normally distributed with a mean of 140.3 feet and a standard deviation of 6.5 feet. Find the probability that the full height of a randomly selected tree is less than 146.8 feet.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Let xx represent the full height of certain species of tree. Assume that xx is normally distributed with a mean of 140.3 feet and a standard deviation of 6.5 feet.

Find the probability that the full height of a randomly selected tree is less than 146.8 feet.

Enter your answer as a number accurate to 4 decimal places.

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Expert Solution

Step 1

The variable x is the full height of certain species of tree which follows normal distribution with mean 140.3 feet, and standard deviation 6.5 feet.

The probability that the full height of a randomly selected tree is less than 146.8 feet is,

$\begin{array}{rcl} P (x < 146.8) & = & P (\frac{x - μ}{σ} < \frac{146.8 - 140.3}{6.5}) \\ = & P (z < \frac{6.5}{6.5}) \\ = & P (z < 1) \end{array}$

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