Answered: A population of values has a normal…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A population of values has a normal distribution with μ=186.8 and σ=70.5. You intend to draw a random sample of size n=41. Please show your answers as numbers accurate to 4 decimal places.

Find the probability that a single randomly selected value is between 197.8 and 198.9.
P(197.8 < X < 198.9) =

Find the probability that a sample of size n=41 is randomly selected with a mean between 197.8 and 198.9.
P(197.8 < x < 198.9) =

Expert Solution

Step 1

A z-score represents the position of a data point in terms of its distance from the mean when measured in standard deviation units, i.e, how far the observation is from the mean in units of standard deviation.

The z of a variable (x) is the ratio of the difference of mean $μ$ from the data point (x) by the standard deviation $σ$ , i.e, $z = \frac{x - μ}{σ}$

For x=197.8

$\begin{array}{rcl} z & = & \frac{197.8 - 186.8}{70.5} \\ = & 0.16 \end{array}$

For x=198.9

$\begin{array}{rcl} z & = & \frac{198.9 - 186.8}{70.5} \\ = & 0.17 \end{array}$

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