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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.5 - Problem 22e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.5 - Problem 22e

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# The morality of a solution in defined to be the number of ISBN: 9780073401331 38

## Solution for problem 22E Chapter 4.5

Statistics for Engineers and Scientists | 4th Edition

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Problem 22E

Problem 22E

The morality of  a solution in defined to be the number  of moles of solute per liter of solution (1 mole=6.02×1023 molecules).if X is the morality of a solution of  sodium choride(NaCl),and Y is the morality of  a solution of sodium carbonate (Na2CO3) the morality of sodium ion (Na+),in a solution made of equal parts NaCl and Na2CO3 is given by M=0.5X+Y. Assume X and Y are independent and normally distributed, and that X has mean 0.450 and standard deviation 0.050,and Y has mean 0.025.

a.         What is the distribution of M?

b.         Find P(M >0.5)

Step-by-Step Solution:
Step 1 of 3

Solution 22E

Step1 of 3:

We have random variable X it presents the morality of a solution of  sodium chloride(NaCl) and another random variable Y presents the the morality of  a solution of sodium carbonate

( ). Let us assume that X and Y are independent and normally distributed, here X has mean and standard deviation and Y has mean and standard

deviation M is solution made of equal parts NaCl and That is

M = 0.5X + Y.

Here our goal is:

a).We need to find the distribution of M.

b).we need to find P(M > 0.5).

Step2 of 3:

a).

As per the given information we assume that X and Y are independent and normally distributed so, as per the property of normal distribution that is “Linear combination of independent and normally distributed variables is also normally distributed.”

Therefore, X and Y are independent and normally distributed hence M is also normally distributed.

That is M N( , )

Where,

1). = E(M)

Substitute M value in above equation we get = E(0.5X+Y)

= 0.5E(X) + E(Y)

= 0.5 + = 0.5(0.450) + 0.250

= 0.225 + 0.250

= 0.475

Hence, = 0.475.

2). = Var(M)

Substitute M value in above equation we get = Var(0.5X+Y)

= 0.5Var(X) + Var(Y)

= = = 0.25(0.0025) + 0.000625

= 0.000625 + 0.000625

= 0.00125

Hence, = 0.00125

3). = = 0.0353

Hence, = 0.0353.

Step3 of 3:

b).

Consider,

P(M > 0.5) = 1 - = 1 - = 1 - = 1 - Here is obtained from standard normal table(area under normal curve) = 0.7580 (In statistical table we have to see row 0.7 under column 0.00)

Now,

= 1 - = 1 - 0.7580

= 0.2420

Hence, P(M > 0.5) = 0.2420.

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

This full solution covers the following key subjects: solution, Morality, sodium, nacl, mean. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 22E from 4.5 chapter was answered, more than 406 students have viewed the full step-by-step answer. The answer to “The morality of a solution in defined to be the number of moles of solute per liter of solution (1 mole=6.02×1023 molecules).if X is the morality of a solution of sodium choride(NaCl),and Y is the morality of a solution of sodium carbonate (Na2CO3) the morality of sodium ion (Na+),in a solution made of equal parts NaCl and Na2CO3 is given by M=0.5X+Y. Assume X and Y are independent and normally distributed, and that X has mean 0.450 and standard deviation 0.050,and Y has mean 0.025.a. What is the distribution of M?________________b. Find P(M >0.5)” is broken down into a number of easy to follow steps, and 94 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 22E from chapter: 4.5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331.

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