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
sergij07 [2.7K]
3 years ago
11

suppose X and Y are independent random variables, both with normal distributions. If X has a mean of 45 with a standard deviatio

n of 4 and Y has a mean of 35 with a standard deviation of 3, what is the probability that a randomly generated value of X is greater than a randomly generated value of Y
Mathematics
1 answer:
djyliett [7]3 years ago
4 0

Answer:

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question:

\mu_X = 45, \sigma_X = 4, \mu_Y = 35, \sigma_Y = 3

What is the probability that a randomly generated value of X is greater than a randomly generated value of Y

This means that the subtraction of X by Y has to be positive.

When we subtract two normal variables, the mean is the subtraction of their means, and the standard deviation is the square root of the sum of their variances. So

\mu = \mu_X - \mu_Y = 45 - 35 = 0

\sigma = \sqrt{\sigma_X^2+\sigma_Y^2} = \sqrt{25} = 5

We want to find P(X > 0), that is, 1 subtracted by the pvalue of Z when X = 0. So

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

Z = \frac{0 - 10}{5}

Z = -2

Z = -2 has a pvalue of 0.0228

1 - 0.0228 = 0.9772

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

You might be interested in
Simplify root 32-6 divided by root 2 plus root 2​
Alex777 [14]

Answer:

5•362165924

Step-by-step explanation:

first make root of 32-6=5•099019514

then make root of 2+root2=1•84--

then divide upper by lower part answer comes

or

root32-6=root26

root 2+root 2=2root2

root26/root2root2

ans=3•0318---

7 0
2 years ago
Read 2 more answers
What is x+3y=6 what is the x
Ymorist [56]
X=-3y+6 That is the answer.
3 0
3 years ago
hello! i struggle with math A LOT so if u guys can help me with these questions with the work i would appreciate a lot
elena-s [515]
Pretty sure 1 is 6/8
4 0
3 years ago
Read 2 more answers
Marry used ¼ litres of cooking oil this week and left with ½ litres. How much cooking oil Marry has at the beginning of the week
Black_prince [1.1K]

Answer:

3/4

Step-by-step explanation:

5 0
3 years ago
Samantha evaluates the expression -5.3 + 7.9 and gets an answer of 2.4
Sholpan [36]

Answer:

Step-by-step explanation:

To the evaluate -5.3+7.9

We get

2.6

Therefore the error

=2.6-2.4

=0.2

6 0
3 years ago
Read 2 more answers
Other questions:
  • In simplest form, which mixed number is equivalent to 22\8
    5·1 answer
  • Which of the following are characteristics of the graph of the quadratic parent function
    13·2 answers
  • Find the equation of a line passing through ( -1/2,1/2) with a slope of 5.
    15·2 answers
  • Hi, what is 45+b^78 divided by 67 then times 45^7?
    8·1 answer
  • What is the missing numbers in this sequence: , 7, 5, 3, , -1
    13·1 answer
  • HELP ME PLS I BEG U!!! The data points for equation A are graphed on the coordinate plane below and are connected by using a str
    12·1 answer
  • How many solutions does the system have? 4x-2y=8 2x+y=2
    10·1 answer
  • WILL BE MARKED BRAINLIEST! What is the median for the following set of numbers? 11,12,11,13,13
    8·1 answer
  • PLEASE HELP ME ASAP!!!!!!!!<br><br><br> ty :)
    11·2 answers
  • These are confusing can anyone help with this?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!