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
Inessa [10]
3 years ago
9

The outcome X of an experiment has only two possible values, X= 4 and X= 5. Given that the expected outcome E(X)= 4.2, find P(X=

5). Give your answer as a decimal.
Mathematics
1 answer:
alukav5142 [94]3 years ago
3 0

Answer:

P(X=5) = 0.2

Step-by-step explanation:

Expected outcome, E(x) = ∑XP(X)

∑ = Summation

X = outcomes

P(X) = probability of an outcome

E(X) = (4*P(X=4)) + (5*P(X=5)) = 4.2

So, 4P(X=4) + 5P(X=5) = 4.2  ... equation 1

But the sum of probabilities = 1

That is, P(X=4) + P(X=5) = 1 ... equation 2

Thus, we have the following system of equations

4P(X=4) + 5P(X=5) = 4.2  ... equation 1

P(X=4) + P(X=5) = 1 ... equation 2

Multiply equation 2 by 4

4*P(X=4) + 4*P(X=5) = 4*1

4P(X=4) + 4P(X=5) = 4  ... equation 3

4P(X=4) + 5P(X=5) = 4.2  ... equation 1

4P(X=4) + 4P(X=5) = 4  ... equation 3

Subtract equation 3 from 1

4P(X=4) - 4P(X=4)  + 5P(X=5) - 4P(X=5) = 4.2 - 4

P(X=5) = 0.2

You might be interested in
A towns population grew from 7500 people to 8210 over the span of 10 years. What is the rate of growth in people per year for th
lisov135 [29]

Answer: 71 people per year

Step-by-step explanation:

8210 - 7500 = 710

710 ÷ 10 = 71.

Rate of growth in people per year for those 10 years = 71 people per year.

7 0
3 years ago
Evaluate g(n- 7) if g(x) = x^2-6/7x
noname [10]

Step-by-step explanation:

g(n-7) = (n-7) ^2-6/7 (n-7) = n^2 -14n+49-6/7 n +6= n^2-104/7 n +55

5 0
3 years ago
Police use a radar unit is used to measure speeds of cars on a freeway. The speeds are normally distributed with a mean of 90 km
vagabundo [1.1K]

Answer:

A. P(x≥100)=0.1587

B. P(x≤0)≈0

Step-by-step explanation:

A. Cause we know the distribution of the data, the method used to solve it is called "Normalization" and we need to have the Mean and the Standard deviation of the data. The method consist in the following equation

P(x≤a)=P( z=((x-μ)/σ) ≤ b=((a-μ)/σ) )

Considering <u>μ as the Mean</u> and <u>σ as the Standard deviation</u>. At first, we had a probability in the normal distribution with Mean=90 and STD=10 but <u>that kind of exercises is not meant to find that probability directly but by using this process</u>.

After we normalize the probability, now <u>we have a probability in a specific normal distribution that has Mean=0 and STD=1 and the difference with what we had before is that now we are able to use tools to find probabilities in a normal standard distribution</u>. My favorite of them is a chart that show the approximate values of a lot of probabilities (i attached it to this answer). I´m going to explain point A as an example:

We look for the probability that P(x≥100), but we don´t have an easy method to use there, so we normalize:

P(x≥100)=P( (x-μ)/σ ≥ (100-μ)/σ )

P(x≥100)=P( z ≥ (100-90)/10 )

P(x≥100)=P( z ≥ 1 )

And now we are able to use the chart, let me explain: First, the chart only works with P(z ≤ b), so we have to change it with properties of probabilities before using the table.

P(z≥1)=1-P(z≤1)

And finally we use the chart:

<u>the value of P(z≤1) is in the table, we look for the row with +1 and the column with the decimal part (in this case 0) and with coordinates (1,0) there´s the value</u>:

P(z≤1)=0.8413

But we need P(z≥1) so we use the previous equality

P(z≥1)=1-P(z≤1)

P(z≥1)=1-0.8413

P(z≥1)=0.1587

Because P(x≥100)=P(z≥1), our final answer is 0.1587

B. We use the same process to try to understand what the probability of P(x≤0) represents.

P(x≤0)=P(z≤ (0-90)/10)

P(x≤0)=P( z ≤ -9 )

But when we try to look for its value in the chart It isn´t even there, what could it mean?

<u>A normal distribution function is always increasing</u>, that means that "a≤b if and only if P(x≤a) ≤ P(x≤b)". so we conclude:

P(z≤-9) ≤ P(z≤-3) (The lowest probability in the chart)

P(z≤-9) ≤ 0.0013

P(z≤-9) is way lower than 0.0013 (they aren´t even close) but we know that probability is always positive,  and because of that:

P(x≤0)=P(z≤-9)≈0

5 0
3 years ago
How could you model 5 students sharing 4 bags of popcorn equally? How much will each student get?
qwelly [4]
One and a fourth bags of popcorn
4 0
3 years ago
A dog buried 18 bones in his backyard. On Monday, he dug up 1/2 of his bones. On Tuesday, he dug up another 1/3 of his bones. Ho
Korolek [52]

Answer:

3

Step-by-step explanation:

A dog buried 18 bones

On Monday he dug up 1/2 of the bones

On Tuesday he dug up 1/3 of the bones

= 1/2 × 18

= 9

= 1/3×18

= 6

Therefore the remaining bones still buried in the ground can be calculated as follows

= 9+6

= 15

= 18-15

= 3

Hence 3 bones are still buried in the ground

5 0
2 years ago
Other questions:
  • Write the slope intercept form of the equation of the line through the given point with the given slope
    13·1 answer
  • A triangle with an area of 202.5 has a height that measures 15 find its base
    13·1 answer
  • Marge has saved $350 toward the cost
    7·1 answer
  • a 120 page book has p lines to a page. if the number of lines were reduced by 3 on each page the number of pages would need to b
    12·1 answer
  • Which is bigger 2/5 or 3/10
    5·2 answers
  • A uniform 41.0 kg scaffold of length 6.6 m is supported by two light cables, as shown below. A 74.0 kg painter stands 1.0 m from
    5·1 answer
  • Here are some numbers
    13·1 answer
  • nick was thinking of a number nick halves the number and gets an aswer of 27.3 form an equation with x from the information
    8·1 answer
  • Which of the following equations is equivalent to 36 – 2 = 34? 34 ∙ 2 = 36 34 + 2 = 36 36 + 34 = 2 34 – 2 = 36
    5·1 answer
  • A solid shape is made by joining two cones.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!