On a shopping trip kellen spent $3 on a bus ticket $9 on a book and $5 after the trip . How much money did he start with

Leakage from underground gasoline tanks at service stations can damage the environment. It is estimated that 25% of these tanks

Gnesinka [82]

Answer:

a) 3.75

b) 23.61% probability that fewer than 3 tanks will be found to be leaking

c) 0% the probability that at least 600 of these tanks are leaking

Step-by-step explanation:

For each tank there are only two possible outcomes. EIther they leak, or they do not. The probability of a tank leaking is independent of other tanks. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

To solve question c), i am going to approximate the binomial distribution to the normal.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

It is estimated that 25% of these tanks leak.

This means that $p = 0.25$

15 tanks chosen at random

This means that $n = 15$

a.What is the expected number of leaking tanks in such samples of 15?

$E(X) = np = 15*0.25 = 3.75$

b.What is the probability that fewer than 3 tanks will be found to be leaking?

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134$

$P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668$

$P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0134 + 0.0668 + 0.1559 = 0.2361$

23.61% probability that fewer than 3 tanks will be found to be leaking

c.Now you do a larger study, examining a random sample of 2000 tanks nationally. What is the probability that at least 600 of these tanks are leaking?

Now we have n = 2000. So

$\mu = E(X) = np = 2000*0.25 = 500$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{2000*0.25*0.75} = 19.36$

This probability is 1 subtracted by the pvalue of Z when X = 600. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{600 - 500}{19.36}$

$Z = 5.16$

$Z = 5.16$ has a pvalue of 0.

0% the probability that at least 600 of these tanks are leaking

4 0

3 years ago

4−(−8)= please help i need it now

s344n2d4d5 [400]

Answer:

hope it helps...

- multiplied with another - gives us a +.

While opening a bracket we consider a sign of multiplication. so the equation becomes 4 + 8 which gives us 12. Thus 12 is the answer.

pls give brainliest for the answer

4 0

3 years ago

Read 2 more answers

Give an example of a real-life continuous function.

prisoha [69]

Answer:

Math is a continuous function. It can keep going on and on.

Step-by-step explanation:

Hope I <em><u>Helped!</u></em> :D

3 0

3 years ago

Which are the partial products for 652 × 4 = 2,608

CaHeK987 [17]

Answer:

652 and 4

Step-by-step explanation:

the product is the total

3 0

3 years ago

Let f(x)=ln(3x)+2.5 .

Cerrena [4.2K]

For this case what we should do is evaluate the function in each of the points from 2 to 7 and then find the average.
We have then:
f (x) = ln (3x) +2.5.
f (2) = ln (3 * 2) + 2.5 = 4.291759469
f (3) = ln (3 * 3) + 2.5 = 4.697224577
f (4) = ln (3 * 4) + 2.5 = 4.98490665
f (5) = ln (3 * 5) + 2.5 = 5.208050201
f (6) = ln (3 * 6) + 2.5 = 5.390371758
f (7) = ln (3 * 7) + 2.5 = 5.544522438
Then the average is:
Average = (4.291759469 + 4.697224577 + 4.98490665 + 5.208050201 + 5.390371758 + 5.544522438) / (6) = 5.019472516
nearest hundredth
5.02
Answer:
the average rate of change of f (x) from 2 to 7 is 5.02

5 0

3 years ago

Read 2 more answers