[6.18] ([1] 7.52) resistors to be used in a circuit have average resistance 200 ohms and standard deviation 10 ohms. suppose 25 of these resistors are randomly selected to be used in a circuit. a) what is the probability that the average resistance for the 25 resistors is between 199 and 202 ohms? b) find the probability that the total resistance does not exceed 5100 ohms.

a)  0.5328   b) 0.9772

Step-by-step explanation:

Given : Resistors to be used in a circuit have average resistance 200 ohms and standard deviation 10 ohms.

  and  

We assume that the resistance in circuits are normally distributed.

a) Let x denotes the average resistance of the circuit.

Sample size : n= 25

Then, the probability that the average resistance for the 25 resistors is between 199 and 202 ohms :-

b) Total resistors = 25

Let Z be the total resistance of 25 resistors.

To find P(Z≤5100 ohms) , first we find the mean and variance for Z.

Mean= E(Y) = E(25 X)=25 E(X)=25(200)= 5000 ohm

The probability that the total resistance does not exceed 5100 ohms will be :

Hence, the probability that the total resistance does not exceed 5100 ohms = 0.9772

final answer is : )

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.