Recall that given a probability of defective tires p, we can model the number of defective tires as a binomial random variable. For 3000 tires, if we have a probability p of having a defective tire, the expected number of defective tires is 3000p.

Let X be the number of defective tires. We can use the total expectation theorem, as follows: if there are $A_1,\dots, A_n$ events that partition the whole sample space, and we have a random variable X over the sample space, then

$E(X) = p(A_1)E(X|A_1) + \dots + p(A_n)E(X|A_n)$ .

So, in this case, we have the following

$E(X) = P(p=0\%)E(X|p=0\%)+P(p=1\%)E(X|p=1\%)+P(p=2\%)E(X|p=2\%)+P(p=3\%)E(X|p=3\%) = 0.1\cdot 3000\cdot 0 + 0.3\cdot 3000\cdot 0.01+ 0.4\cdot 3000\cdot 0.02+ 0.2\cdot 3000\cdot 0.03 = 51$ .

Let Y be the number non defective tires. then X+Y = 3000. So Y = 3000-X. Then E(Y) = 3000-E(X). Then, E(Y) = 2949.

Finally, note that the cost of the batch would be 40Y+45X. Then

$E(40Y+45X) = 40E(Y)+45E(X) = 40\cdot 2949+45\cdot 51=120255$

3 0

4 years ago

This morning, Carmen's car had 29.03 gallons of fuel. Now, 2.9 gallons are left. How much fuel did Carmen use?

ankoles [38]

Answer:

I hope my answer is right but im pretty sure its 26.13 :)

Step-by-step explanation:

6 0

3 years ago

How do you divide a fraction

sveta [45]

Hey, 25equivelv!

If you know how to multiply a fraction, you will be able to divide it as well. If you do not know how to multiply a fraction, look it up or message me.

I say that if you know how to multiply fractions you know how to divide them because dividing is basically multiplication backwards, so in fraction terms, it's multiplying by the reciprocal. If you don't know what that is, multiplying by the reciprocal is that same as flipping the second fraction and multiplying.

Watch this youtube video for more: https://www.youtube.com/watch?v=q4vEI4mk8g0

Hope I helped!

~Olivia

8 0

3 years ago

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