Compare 0.14 and 0.014

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

What is the square root of -1?

asambeis [7]

Answer:

The answer would be 1, whenever you square a negative number you should just input it as positive. The answer would be the same.

Step-by-step explanation:

4 0

3 years ago

The volume of a solid is 192 cm if the height is 6 cm and the length is 8 cm find the width

bezimeni [28]

Answer:

Step-by-step explanation:

V=a*b*c

192= 8*b*6

b=192/48

b= 4 cm

6 0

3 years ago

At the bike shop x, it cost $2.75 per hour plus a $3.00 deposit to rent a bike.AT Bike shop z cost $1.75 per hour plus a $7.00 d

Alex_Xolod [135]

Multiply the rate per hour by the number of hours (n) and add the deposit.

A)

Bike shop x: c = 2.75n + 3.00

Bike shop z: c = 1.75n + 7.00

B) to find when they will cost the same set the equations equal to each other and solve for n:

2.75n + 3.00 = 1.75n + 7.00

Subtract 3 from each side:

2.75n = 1.75n + 4.00

Subtract 1.75n from both sides:

1.00n = 4.00

Divide both sides by 1:

n = 4 hours

6 0

4 years ago

A golf ball is hit in not the air represented by the equation y= -3x^2+18x+45. The maximum height the ball will reach is____ fee

Temka [501]

Answer:

72 ft

Step-by-step explanation:

Here, we want to get the maximum height the ball will reach

the maximum height the ball will reach is equal to the y-coordinate of the vertex of the equation

So we need firstly, the vertex of the given quadratic equation

The vertex can be obtained by the use of plot of the graph

By doing this, we have it that the vertex is at the point (3,72)

Thus, we can conclude that the maximum height the ball can reach is 72 ft

3 0

3 years ago