Answered: 6. What is the probability that ho…

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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Transcribed Image Text:b Answered: A X CA Sludy Repor x G The diamieter of. x CThe Diameter Er xX Mathway Alger x * chegg com/homework-help/questions-and-answers/diameter brand tenis balls appteximately-normally- PM FIT LMP Community E Truth Table Genetat. 6 e MerrickBank Corp 3 Tiger Algebra bartieby EStatistics Calculator 5. What is the probability that the sample mean is less then 2.74 inchen? Save PÔX<274)= Reund to four decimal places as reeded.) D0 pts e Whal is the probability that the sample mean is tetween 2.75 aed 278 nchas? P275<X<279)= Round to fou decimal places as needec ) d The probablity is $8% thal the sample mean will be between what two values symmerically distributedFaround the population mean? The lower bound i Round to two decimal places as needed ). inches The upper boued is inches

Transcribed Image Text:7.2.7-T E Question Help The diameter of a brand of tennis balls is approOximately normally distributed, with a mean of 2.76 inches and a standard deviation of 0.05 inch. A random sample of 12 tennis balls is selected. Complete parts (a) through (d) below.

Expert Solution

Step 1

From the given information,

Mean=2.76

Standard deviation = 0.05

Sample size =12

The probability that the sample mean is less than 2.74 inches is calculated as follows:

$\begin{array}{rcl} P (X < 2.74) & = & P (\frac{X - μ}{\frac{σ}{\sqrt{n}}} < \frac{2.74 - 2.76}{\frac{0.05}{\sqrt{12}}}) \\ = & P (z < - 1.39) \\ = & 0.08226 \end{array}$

The probability that the sample mean is less than 2.74 inches is 0.0823.

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