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4 years ago

Please help this is urgent and I am being timed

Mathematics

1 answer:

Shkiper50 [21]4 years ago

5 0

Hi there!

Pauline simplified the expression correctly.

Pauline made sure she used the distributive property and combined like terms after doing so.

Hope this helps !

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Height of Dutch Men. Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeter

trapecia [35]

Answer:

a) $P(X$

$P(z$

b) $P(X>195) =P(Z>\frac{195-183}{10.5})=P(Z>1.143)$

$P(z>1.143)=1-P(Z$

c) $P(173$

$P(-0.953$

d) $P(\bar X >190)=P(Z>\frac{190-183}{\frac{10.5}{\sqrt{1000}}}=21.08)$

And using a calculator, excel ir the normal standard table we have that:

$P(Z>21.08)=1-P(Z$

So for this case we expect anyone with a heigth higher than 190 cm in a random sample of 1000.

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".

Part a

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

$X \sim N(183,10.5)$

Where $\mu=183$ and $\sigma=10.5$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability with the normal standard table or with excel:

$P(z$

Part b

$P(X>195)$

$P(X>195) =P(Z>\frac{195-183}{10.5})=P(Z>1.143)$

And we can find this probability with the normal standard table or with excel: using the complement rule

$P(z>1.143)=1-P(Z$

Part c

$P(173$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(173$ And we can find this probability on this way:

$P(-0.953$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-0.953$ Part d

Since the distributiion for X is normal then the distribution for the sample mean is also normal and given by:

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

And we eant this probability:

$P(\bar X >190)=P(Z>\frac{190-183}{\frac{10.5}{\sqrt{1000}}}=21.08)$

And using a calculator, excel ir the normal standard table we have that:

$P(Z>21.08)=1-P(Z$

So for this case we expect anyone with a heigth higher than 190 cm in a random sample of 1000.

3 0

3 years ago

A motorcycle costs 12000. The value of the motorcycle deceases 6% each year. What is the rate each month

quester [9]

There are 12 months in a year and each year it decreases 6% so therefore each month it decreases .5%.

If you were asking the the amount it depreciates each month then you take .5% or .005 of 12000 which is 60 dollars a month.

7 0

3 years ago

Read 2 more answers

Marie gets paid $ 2,000 monthly and a commission of 50 dollars for each sale she makes. Write an expression that represents her

denpristay [2]

Answer:

2000+(50× x)

Step-by-step explanation:

The certain salary is 2000 but we do not know how much sale where made so the amount is placed as x inwhich will be multiples by 50 then added to 2000 to get total

8 0

3 years ago

For f(x) = x^2, find f(4 - sqrt(2))

ryzh [129]

$\bf f(x)=x^2\qquad f(4-\sqrt{2})\implies x=4-\sqrt{2}
\\\\\\
f(4-\sqrt{2})=\left( 4-\sqrt{2} \right)^2\implies f(4-\sqrt{2})=\left( 4-\sqrt{2} \right)\left( 4-\sqrt{2} \right)$

do a FOIL on it to get the product, or just use the binomial theorem to expand the binomial and simplify

4 0

3 years ago

Choose the formula for the volume of a rectangular box, V = lwh written in terms of w.

lilavasa [31]

The width of the rectangular box will be 8cm

Given that the formula for calculating the volume of a rectangular box is expressed as:

$V=lwh$