Answered: The length of a fully grown hibiscus…

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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Question

The length of a fully grown hibiscus plant is normally distributed and has a mean 35cm. It is found that 5% of these plants are longer than 45cm.

i. Find the standard deviation σ. [4]

ii. When plants are chosen for sale, those shorter than 30cm are rejected. Find the probability that a plant will be rejected.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

Given Information

Mean µ = 35

5% of the plants are longer than 45 cm means

P(X>45) =0.05

P (Z > z) = 0.05

P(Z <z) = 1 – 0.05 =0.95

First we need to find the standard deviation

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