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2 years ago

A shopping club is having a a sale. members and non-members of the club recieve different discounts, as shown below

Mathematics

1 answer:

lana [24]2 years ago

5 0

Answer:

Step-by-step explanation:

580 - 58 (10% of 580) = 522

522 - discount price (20) = 502

Sally is paying 502 for her camcorder

990 - 247.5 (25% of 990) = 742.5

742.5 - 20 = 722.5

Sally is paying $502

Tabitha is paying $722.5

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A grinding wheel manufacturer designed a new grinding wheel. Repeated tests were conducted on wheels of approximately the same w

sergejj [24]

Answer:

a) $a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

b) $P(X \geq 3) = 1-P(X$

c) $P(\bar X \geq 225)=1- P(\bar X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Part a

Let X the random variable that represent the cuts of a population, and for this case we know the distribution for X is given by:

$X \sim N(225,16.5)$

Where $\mu=225$ and $\sigma=16.5$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.674=\frac{a-225}{16.5}$

And if we solve for a we got

$a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

Part b

For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:

$X\sim Bin(n=10, p=0.25)$

And we want this probability:

$P(X \geq 3) = 1-P(X$

We can find the individual probabilities like this:

$P(X=0)=(10C0)(0.25)^0 (1-0.25)^{10-0}=0.0563$

$P(X=1)=(10C1)(0.25)^1 (1-0.25)^{10-1}=0.1877$

$P(X=2)=(10C2)(0.25)^2 (1-0.25)^{10-2}=0.2816$

$P(X \geq 3) = 1-P(X$

Part c

For this case we know that the distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we want this probability:

$P(\bar X \geq 225)$

And for this case we can use the complement rule and the z score given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we replace we got:

$P(\bar X \geq 225)=1- P(\bar X$

4 0

2 years ago

The mean income per person in the United States is $44,500, and the distribution of incomes follows a normal distribution. A ran

Artist 52 [7]

Answer:

We conclude that the residents of Wilmington, Delaware, have higher income than the national average

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $44,500

Sample mean, $\bar{x}$ = $52,500

Sample size, n = 16

Alpha, α = 0.05

Sample standard deviation, s = $9,500

a) First, we design the null and the alternate hypothesis

$H_{0}: \mu = 44,500\text{ dollars}\\H_A: \mu > 44,500\text{ dollars}$

We use one-tailed(right) t test to perform this hypothesis.

c) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{52500 - 44500}{\frac{9500}{\sqrt{16}} } = 3.37$

b) Rejection rule

If the calculated t-statistic is greater than the t-critical value, we fail to accept the null hypothesis and reject it.

Now,

$t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis. We conclude that the residents of Wilmington, Delaware, have higher income than the national average

5 0

2 years ago

If a = 8 in and b = 15 in what is the length of leg c in a right triangle using the

laila [671]

So a²+b²=c²
8²+15²=c²
64+225=c²
289=c²
±17=c
So c=17 or c=-17

4 0

2 years ago

Read 2 more answers

How many cords of wood could you fit in a room that is 4 yards long, 4 yards wide, and 2 yards high?

Anuta_ua [19.1K]

Hi there!

It depends on the dimensions of each cords of wood. If each cord of wood is just one square yard large, then you could fit 4*4*2=32 cords of wood into a room that has the dimensions that you described.

-AwesomeRepublic :)

6 0

2 years ago

Two standard 6-sided number cubes are rolled, a red one and a blue one. How many different sums are possible?

AlladinOne [14]

Answer:

There are 11 different sums.

Step-by-step explanation:

When you roll two dice, the smallest number you can get is 2, and the largest 12, and you can get all in between. So 12-2 is equal to 10, but we have to add another 1 because 2 counts. So the answer is 11.

8 0

2 years ago