1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Andreyy89
3 years ago
12

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

s (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm.a.What is the probability that a Dutch male is shorter than 175 cm?b.What is the probability that a Dutch male is taller than 195 cm?c.What is the probability that a Dutch male is between 173 and 193 cm?d.Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?
Mathematics
1 answer:
trapecia [35]3 years ago
3 0

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

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(173And 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(-0.953Part 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.

You might be interested in
I surveyed students in my Math II classes to see how many hours of television they watched the night before our big test on tria
Oduvanchick [21]
Given the table below representing the number of hours of television nine Math II class students watched the night before a big test on triangles along with the grades they each earned on that test.

\begin{center}
\begin{tabular}
{|c|c|}
Hours Spent Watching TV & Grade on Test (out of 100)  \\ [1ex]
4 & 71 \\ 
2 & 81 \\ 
4 & 62 \\ 
1 & 86 \\ 
3 & 77 \\ 
1 & 93 \\ 
2 & 84 \\ 
3 & 80 \\ 
2 & 85
\end{tabular}
\end{center}

Let the number the number of hours of television each of the students watched the night before the test be x while the grades they each earned on that test be y.

We use the following table to find the equation of the line of best fit of the regression analysis of the data.

\begin{center} \begin{tabular} {|c|c|c|c|} x & y & x^2 & xy \\ [1ex] 4 & 71 & 16 & 284 \\ 2 & 81 & 4 & 162 \\ 4 & 62 & 16 & 248 \\ 1 & 86 & 1 & 86 \\ 3 & 77 & 9 & 231 \\ 1 & 93 & 1 & 93 \\ 2 & 84 & 4 & 168 \\ 3 & 80 & 9 & 240 \\ 2 & 85 & 4 & 170 \\ [1ex]\Sigma x=22 & \Sigma y=719 & \Sigma x^2=64 & \Sigma xy=1,682 \end{tabular} \end{center}

Recall that the equation of the line of best fit of a regression analysis is given by
y=a+bx
where:
a= \frac{(\Sigma y)(\Sigma x^2)-(\Sigma x)(\Sigma xy)}{n(\Sigma x^2)-(\Sigma x)^2}
and
b= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{n(\Sigma x^2)-(\Sigma x)^2}

y=\frac{(719)(64)-(22)(1,682)}{9(64)-(22)^2}+\frac{9(1,682)-(22)(719)}{9(64)-(22)^2}x \\  \\ = \frac{46,016-37,004}{576-484} + \frac{15,138-15,818}{576-484} x \\  \\ = \frac{9,012}{92} + \frac{-680}{92} x \\  \\ =97.95-7.391x

Thus, the equation of the line of best fit is given by y = 97.95 - 7.391x

<span>A student that watched 1.5 hours of TV will have a score given by
y = 97.95 - 7.391(1.5) = 97.95 - 11.0865 = 86.8635

Therefore, </span><span>a student’s score if he/she watched 1.5 hours of TV to the nearest whole number is 87.</span>
6 0
3 years ago
What is the answer in scientific notation
chubhunter [2.5K]
The answer would be 3 times 10^-5
5 0
2 years ago
Help me please if you can
makvit [3.9K]

Answer:

-2

Step-by-step explanation:

Add them up: -14

Divide by how many there are: -14 / 7 = -2

4 0
2 years ago
Please help I don’t know how to-
aivan3 [116]

Answer:

y is going back by 3's x is going back one

Step-by-step explanation:

3 0
3 years ago
Mary's 3 hamsters each eat three-eighths of cup of grain a day, if she has 6 and 3/4 cups of grain, how many days will the grain
muminat
Hello!

3/8 times 3 equals 9/8 which is also 1 1/8. If you multiply 3/4 by two (numerator and denominator) then you will get 6/8. And if you multiply 9/8( I just find it easier with 9/8) by 6 you will get 54/8. And the grain will last for 6.75 days.

I may be wrong let me know.
Hope this helps!
5 0
3 years ago
Read 2 more answers
Other questions:
  • 30 POINTS !!!
    15·2 answers
  • Original price of a computer is 500$ tax is 6% what is the selling price
    13·2 answers
  • A music player was marked down by 1/4 of the original price.
    6·2 answers
  • Mrs. Cousins works in a pool store and earns a 9.5% commission on every swimming pool she sells. How much commission would she e
    5·1 answer
  • Find the number that belongs<br> in the green box.<br><br> Round your answer to the nearest tenth.
    9·2 answers
  • For each inequality, decide whether the solution is represented by x &lt; 4.5 or x &gt; 4.5.
    6·1 answer
  • What is the value of x in triangle PQR below?
    6·1 answer
  • What is the value of x in this diagram?<br><br> I need this ASAP!!!
    11·1 answer
  • CAN ANYBODY PLEASE HELP ME FOR BRAINLIEST, I'VE BEEN ASKING FOR DAYS AND POSTING DAILY THE SAME QUESTION :(
    7·1 answer
  • when asked to factor the x^2 - 100, a student gives the answer (x -10) (x-10). what is wrong with this answer?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!