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3 years ago

If the shop has 350 fish available for sale, how many of them are goldfish?

Mathematics

2 answers:

Otrada [13]3 years ago

6 0

Answer:

105 fish my dear

Step-by-step explanation:

Lina20 [59]3 years ago

3 0

Answer:

105

Step-by-step explanation:

multiply 350 by .30(30%) and that will tell you how many goldfish there are

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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 3.75x-5-8.75+4.5+0.5 I need help ASAP it is a simplify the expression question

miv72 [106K]

Answer:

3.75x-8.75 or

Step-by-step explanation:

3 0

3 years ago

A customer owes $33.63 in transaction fees and he/she gives you $40.00. how much change should the customer receive back?

Nataliya [291]

The customer should receive $6.37 back

3 0

3 years ago

You are a supervisor for a home cleaning business,

irinina [24]

Answer:

option a

Step-by-step explanation:

i think this because my teacher in my business class stated this before to the whole class but I was distracted so it can totally be wrong if it is my bad

8 0

2 years ago

Describe at least two similarities between constructing a perpendicular line through a point on a line and constructing a perpen

Sophie [7]

Two similarities between constructing a perpendicular line through a point on a line and constructing a perpendicular through a point off a line are;

1. Arcs are drawn to cross the given line twice on either side relative to the point

2. The perpendicular line is drawn using a straight edge by connecting the small arcs formed using the arcs from step 1, to the point on the line or off the line

Description:

1. One of the first steps is to place the compass on the point and from

point, draw arcs to intersect or cross the given line at two points.

2. The compass is placed at each of the intersection point in step 1 and

(opened a little wider when constructing from a point on the line) arcs are

drawn on one (the other side of the point off the line) side of the line with

the same opening (radius) of the compass to intersect each other.

3. From the point of intersection of the arcs in step 2, a line is drawn with a

straight edge passing through the given point.

Learn more about perpendicular lines here:

brainly.com/question/11505244

8 0

2 years ago