Recently, it was found that the length of months that cell phones last is 24.42 months, with astandard deviation of 2.73 months. It is known that the distribution of lengths of cell phones isnormally shaped.State the random variable.O1 = the average length of months cell phones lastOI = the average length of months cell phones lastOr = the length of months a cell phone lastsO= the length of months a cell phone lastsFind the probability that the length of months that cell phones last is from 24 to 30 months.Round to three decimal places.Which is the notation for this probability?O P(24 < < 30)O P(24 < I < 30)Find the probability that the average length of months cell phones last is from 24 to 30 monthsfor a sample of size 32. Round to three decimal places.Which is the notation for this probability?OP(24 < 30)OP(24 < 30)

Answered: Recently, it was found that the length…

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

Recently, it was found that the length of months that cell phones last is 24.42 months, with a
standard deviation of 2.73 months. It is known that the distribution of lengths of cell phones is
normally shaped.
State the random variable.
O1 = the average length of months cell phones last
OI = the average length of months cell phones last
Or = the length of months a cell phone lasts
O= the length of months a cell phone lasts
Find the probability that the length of months that cell phones last is from 24 to 30 months.
Round to three decimal places.
Which is the notation for this probability?
O P(24 < < 30)
O P(24 < I < 30)
Find the probability that the average length of months cell phones last is from 24 to 30 months
for a sample of size 32. Round to three decimal places.
Which is the notation for this probability?
OP(24 < 30)
OP(24 < 30)

Expert Solution

Step 1

A normal distribution follows a bell shaped curve which is centred at the mean and it is also called Gaussian distribution. The normal distribution with 0 mean and 1 standard deviation is called standard normal distribution.

The relation between a normal random variable x and z-score is $z = \frac{x - μ}{σ}$ , where $μ$ is mean and $σ$ is standard deviation of x. The proportion of data that lies in an interval is equal to the area of that interval.

According to central limit theorem the sampling distribution of sample mean follows the normal distribution if the population is normal or the sample size is at least 30. The mean of the sampling distribution is equal to population mean and the standard deviation (also called standard error) is $\frac{σ}{\sqrt{n}}$ .