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
Determine which fraction is greater. 11 over 15 comma 14 over 27
Evgen [1.6K]
11/14 is bigger than 14/27
8 0
3 years ago
Helen paid $246 for three jeans from her favourite clothing store. How much did she pay for each jeans she bought?
Natali5045456 [20]

Answer:

estimate: $80

exact amount paid: $82

Step-by-step explanation:

If you round $246 to 240, then divide it by 3, you should get $80. The cost per pair should be around $80 each

For the exact answer you take the amount spent (246) and divide it by the amount of jeans she bought (3).

246/3 = 82

7 0
3 years ago
SOMEONE PLEASE HELP!!!!!!!!!!!!!!!!!!1
UkoKoshka [18]

the answer is 5 if you need an explanation ask for it in the comments

8 0
3 years ago
Read 2 more answers
If X is a rational number and Y is the opposite of X, why do X and Y have the same absolute value
blsea [12.9K]
Because they are both values
4 0
3 years ago
Help me. i swear... if u dont. u are an uncultured swine
igor_vitrenko [27]

Answer:

a

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • A salesman has a 20% chance of a sale at his first stop, a 30% chance of a sale at his second stop and a 16% chance of a sale at
    7·1 answer
  • A Gardner bought 300 square meters of sod for her yard if the yard has a length of 20 meters how wide a section of your yard can
    10·1 answer
  • What do scientists usually do if they can't draw clear conclusions?
    7·1 answer
  • What is the order pair for x+y=4 and x= -1
    14·1 answer
  • Select the fraction that is equivalent to 0.0368.
    14·1 answer
  • How do you solve 3(1+5)
    11·2 answers
  • 25 POINTS!! State the minimum monthly income and hourly wage per worker needed to cover monthly expenses for the family you used
    13·1 answer
  • Someone plz help and include an explanation plz cuz I’m a lil confused
    11·2 answers
  • Help I need an awnser
    15·1 answer
  • What are vented rotors? When are they used?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!