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
almond37 [142]
3 years ago
13

5. X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. This can be written as N(8,4). Th

e probability that X is between 1.48 and 15.56 is _____________. Write out the probability notation for this question.
Mathematics
1 answer:
xz_007 [3.2K]3 years ago
5 0

Answer:

The probability that X is between 1.48 and 15.56 is P(1.48 \leq X \leq 15.56) = 0.919

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

X is a normally distributed random variable with a mean of 8 and a standard deviation of 4.

This means that \mu = 8, \sigma = 4

The probability that X is between 1.48 and 15.56

This is the pvalue of Z when X = 15.56 subtracted by the pvalue of Z when X = 1.48. So

X = 15.56

Z = \frac{X - \mu}{\sigma}

Z = \frac{15.56 - 8}{4}

Z = 1.89

Z = 1.89 has a pvalue of 0.9706

X = 1.48

Z = \frac{X - \mu}{\sigma}

Z = \frac{1.48 - 8}{4}

Z = -1.63

Z = -1.63 has a pvalue of 0.0516

0.9706 - 0.0516 = 0.919

Write out the probability notation for this question.

P(1.48 \leq X \leq 15.56) = 0.919

The probability that X is between 1.48 and 15.56 is P(1.48 \leq X \leq 15.56) = 0.919

You might be interested in
Here a brainliest if you get it right
oksian1 [2.3K]

Answer:

D.(2, 2)

Step-by-step explanation:

  • Staring point = (2, -4)
  • Since he moved 6 units up, so, there will be change in only y-coordinate of the starting point and x-coordinate will remain unchanged.
  • End point of the segment = (2, - 4 + 6) = (2, 2)
3 0
2 years ago
A rock climber averages 12 3/5 feet per minute. Write and solve an equation to find how many feet x the rock climber climbs in 3
Nikolay [14]
Set up a proportion. If 12 3/5 feet can be traveled in one minute, then make that a fraction. 12 3/5 over one equals X over 30. Cross multiply 12 3/5×30 equals 1 X and solve.
6 0
3 years ago
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Y_Kistochka [10]

53 and 17

Step-by-step explanation:

If you add 53 and 17, you get 70.

If you subtract 17 from 53, you get 36. Hope this helps!

7 0
3 years ago
Find the inverse of the function and then determine whether the inverse is a function.
klemol [59]

as you already know, we start off by doing a quick switcheroo on the variables, and then we solve for y to get the inverse,


\bf y=x^2+4\implies \stackrel{switcheroo}{x = y^2+4}\implies x-4=y^2\implies \pm\sqrt{x-4}=\stackrel{f^{-1}(x)}{y}


and if you run a vertical line test on that expression, you'll find that it doesn't pass it, meaning is not a function.

7 0
3 years ago
Read 2 more answers
Can anybody help me with this?<br><br> Use this graph of f to find the solutions to f(x) = 0.
Brums [2.3K]
Another way to say f(x) is y, so y=0 at -2 and 10. :)
6 0
3 years ago
Other questions:
  • -5 = 5/10 + z<br> Brainly
    15·1 answer
  • At the doctor’s office, Martin learns that his heart beats 360 times in 5 minutes.How many does his heart beat per minute?
    12·1 answer
  • in the three stacks of books there are 15 books, 9 books and 9 books if the books were rearranged so that the stack had the same
    11·1 answer
  • What major key has the same number of sharps and flats as the key of a minor. A. A major B. F major C. C major D. G major This i
    6·1 answer
  • LSAT test scores are normally distributed with a mean of 152 and a standard deviation of 10. Find the probability that a randoml
    7·1 answer
  • The area if a rectangle is 53.6cm^2.If the length is multiplied by four and the width is halved, the area would then be?
    6·1 answer
  • -9 is less than w and w is less than or equal to -3
    15·1 answer
  • Solve for x. <br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B2%7D%20%20%3D%20%20-%207" id="TexFormula1" title=" \frac{
    7·2 answers
  • Find the solution of the system of equations.<br> -7x - 3y = - 20<br><br> 3x+ 6y = -15
    7·1 answer
  • Let g be the piecewise defined function shown.
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!