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
nika2105 [10]
3 years ago
6

Suppose the heights of women at a college are approximately Normally distributed with a mean of 66 inches and a population stand

ard deviation of 1.5 inches. What height is at the 10 th ​percentile? Include an appropriately labeled sketch of the Normal curve to support your answer.

Mathematics
1 answer:
Kaylis [27]3 years ago
5 0

Answer:

z=-1.28

And if we solve for a we got

a=66 -1.28*1.5=64.08

So the value of height that separates the bottom 10% of data from the top 90% is 64.08.

The graph attached illustrate the situation.

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".  

Solution to the problem

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(66,1.5)  

Where \mu=66 and \sigma=1.5

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

P(X>a)=0.90   (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 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

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=-1.28

And if we solve for a we got

a=66 -1.28*1.5=64.08

So the value of height that separates the bottom 10% of data from the top 90% is 64.08.

The graph attached illustrate the situation.

 

You might be interested in
Subtract and reduce to lowest terms: 4 - 5/8
lord [1]

Answer: 3 3/8

Hope this helps!

7 0
3 years ago
Meghan has a beginning balance of $750 in her checking account. She writes a check for $150 and has a debit transaction of $135.
tatuchka [14]
Her new balance is her new balance would be 435
heres my math 
750-150-135=435
8 0
3 years ago
Read 2 more answers
I’m not sure how to do this problem
strojnjashka [21]
The first one would be x^12
6 0
3 years ago
What is the value of the expression below when x<br> 3 and y = 8?<br> 6x + 10y
suter [353]

Answer:

98

Step-by-step explanation:

So we have the expression:

6x+10y

And we want to evaluate it when x is 3 and y is 8.

So, substitute:

=6(3)+10(8)

Multiply:

=18+80

Add:

=98

And we're done!

7 0
3 years ago
Read 2 more answers
1/4 X Plus x equals negative 3 plus 1/2 x
ElenaW [278]
1/4x+4/4x = -6/2x+1/2x
5/4x = -5/2x
x=0
5 0
3 years ago
Other questions:
  • The tires on your bike have a diameter of 17 inches. how many rotations does each tire make when you travel 600 ft?
    10·1 answer
  • Cara has 25$ to buy dry pet food and treats for the animal shelter. A pound of dog food cost $2 and treats are $1 apiece. If she
    10·1 answer
  • Help with 694 = x10<br><br> and its says write it in scientific notation
    7·2 answers
  • if 4% of packages get lost in the mail, then which decimal best represent the amount of packages lost in the mail?​
    11·1 answer
  • What is 0.4% writen as a decimal, and why thanks :)
    11·2 answers
  • Can you guys helps with these two answers please?
    11·1 answer
  • What is h?<br> Problem 23h=12
    6·2 answers
  • Find the length of side x in simplest radical form with a rational denominator.
    5·1 answer
  • PLS ANSWER ASAP THIS QUESTION IS VERY HARD FOR ME
    11·1 answer
  • -3(x - 1) + 8(x - 3) = 6x + 7 - 5x<br> Please helppp
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!