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
ElenaW [278]
2 years ago
10

Assume the random variable X is normally distributed with mean 53 and standard deviation of 6. Find the 9th percentile

Mathematics
1 answer:
satela [25.4K]2 years ago
6 0

Answer:

<em>The 9th percentile of X is 44.96</em>

Step-by-step explanation:

<u>Percentiles for a Normal Distribution</u>

The standard normal distribution can be used for computing percentiles. For example, the median is the 50th percentile being the center value, the first quartile is the 25th percentile, and so on.

To compute percentiles of a normal distribution we can use the formula

X=\mu+z\sigma

Where \mu is the mean, \sigma is the standard deviation of the variable X, and z is the z-score value from the standard tables

The value of X can also be directly obtained from digital tables included in math packages and tools like Excel.

The Excel NORM.INV Function calculates the inverse of the cumulative Normal Distribution Function for a given value of p, \mu and \sigma.

We'll use the values

p=9\%=0.09,\ \mu=53, \ \sigma=6

NORM.INV(0.09,53,6) results in 44.96 which means the 9th percentile of X is 44.96

We could have used the standard normal distribution, which only needs the value of p

NORM.S.INV( 0.09 )=-1.34

That is the value of z, we now apply the formula

X=\mu+z\sigma

X=53+(-1.34)\cdot 6=44.96

We get the very same result as before

You might be interested in
I need help with this math problem
klemol [59]

Answer:

x = 15

Step-by-step explanation:

The right angle is formed at at the tangent line and the radius

So to solve for the missing angle we can solve for x using the Pythagorean Theorem

The Pythagorean theorem states that the sum of the two legs squared equal the hypotenuse squared

Knowing this we can create an equation to solve for x

12^2+9^2=x^2

now we solve for x

12^2=144\\9^2=81\\81+144=225\\225=x^2\\\sqrt{225} =15\\\sqrt{x^2} =x\\x=15

So we can conclude that x = 15

6 0
3 years ago
I really need help before tomorrow!! Please help me!!
Pavel [41]

Answer:

the answer is 6

Step-by-step explanation:

you take the absolute value for both of them which is 2 and 8 but you keep the negative still so it would be -2+8 which is 6

8 0
3 years ago
Read 2 more answers
Five cards are drawn from a standard 52-card playing deck. A gambler has been dealt five cards—two aces, one king, one 3, and on
Nookie1986 [14]

Answer:

The probability that he ends up with a full house is 0.0083.

Step-by-step explanation:

We are given that a gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards.

We have to find the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind).

We know that gambler will end up with a full house in two different ways (knowing that he has given two more cards);

  • If he is given with two kings.
  • If he is given one king and one ace.

Only in these two situations, he will end up with a full house.

Now, there are three kings and two aces left which means at the time of drawing cards from the deck, the available cards will be 47.

So, the ways in which we can draw two kings from available three kings is given by =  \frac{^{3}C_2 }{^{47}C_2}   {∵ one king is already there}

              =  \frac{3!}{2! \times 1!}\times \frac{2! \times 45!}{47!}           {∵ ^{n}C_r = \frac{n!}{r! \times (n-r)!} }

              =  \frac{3}{1081}  =  0.0028

Similarly, the ways in which one king and one ace can be drawn from available 3 kings and 2 aces is given by =  \frac{^{3}C_1 \times ^{2}C_1 }{^{47}C_2}

                                                                   =  \frac{3!}{1! \times 2!}\times \frac{2!}{1! \times 1!} \times \frac{2! \times 45!}{47!}

                                                                   =  \frac{6}{1081}  =  0.0055

Now, probability that he ends up with a full house = \frac{3}{1081} + \frac{6}{1081}

                                                                                    =  \frac{9}{1081} = <u>0.0083</u>.

3 0
3 years ago
Read 2 more answers
What's 45 out of 58 in percentage?
Vladimir [108]
For \ any \ percentage \ you \ just \ take \ the \ number, \ here \ 45, \\ divide \ by \ the\ number \ here\ 58,\ and \ multiply \ by \ 100 \ \%. \\\\ \frac{45}{58}\cdot 100 \ \%= 0,7758 \cdot 100 \ \%=77,58 \ \% \approx 78 \ \%


5 0
3 years ago
Read 2 more answers
This one is about swings so yeaaa
Tpy6a [65]

Answer:

A

Ratio is 2:1

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • What is the slope of the two points (-2,7) and (4,-8)
    6·2 answers
  • Solve for x<br><br> 2x+3+5x=24 <br> what is x?
    8·1 answer
  • Help with this math problem
    13·2 answers
  • Y = | x |, 4 units right, reflection over x-axis
    11·1 answer
  • Find the value of the expression: −mb −m^2 for m=3.48 and b=96.52
    6·1 answer
  • What<br> is the vaule of the expression to if f = 7?
    11·1 answer
  • What is another name for 23 ten thousands
    5·2 answers
  • What is the value of x ?
    14·1 answer
  • Vicky made some purchases at the
    6·1 answer
  • The equation y = 1.9 x can be used to determine the total weight in pounds, y, of the number of paperback books in the first pri
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!