discrete random variable X has the following probability distribution: x 13 18 20 24 27 P ( x ) 0.22 0.25 0.20 0.17 0.16 Compute each of the following quantities. P ( 18 ) . P(X > 18). P(X ≤ 18). The mean μ of X. The variance σ 2 of X. The standard deviation σ of X.
Answers
Answer:
(a) P(X = 18) = 0.25
(b) P(X > 18) = 0.53
(c) P(X ≤ 18) = 0.47
(d) Mean = 19.76
(e) Variance = 22.2824
(f) Standard deviation = 4.7204
Step-by-step explanation:
We are given that discrete random variable X has the following probability distribution:
X P (x) X * P(x)
* P(x)
13 0.22 2.86 169 37.18
18 0.25 4.5 324 81
20 0.20 4 400 80
24 0.17 4.08 576 97.92
27 0.16 4.32 729 116.64
(a) P ( X = 18) = P(x) corresponding to X = 18 i.e. 0.25
Therefore, P(X = 18) = 0.25
(b) P(X > 18) = 1 - P(X = 18) - P(X = 13) = 1 - 0.25 - 0.22 = 0.53
(c) P(X <= 18) = P(X = 13) + P(X = 18) = 0.22 + 0.25 = 0.47
(d) Mean of X, = ∑X * P(x) ÷ ∑P(x) = (2.86 + 4.5 + 4 + 4.08 + 4.32) ÷ 1
= 19.76
(e) Variance of X, = ∑
* P(x) -
= 412.74 - = 22.2824
(f) Standard deviation of X, =
=
= 4.7204 .
Final answer:
The probabilities for the given X values are calculated by summing the relevant given probabilities. The mean of X is computed as a weighted average, and the variance and standard deviation are calculated using formula involving the mean and the individual probabilities.
Explanation:
The probability P(18) is given as 0.25 according to the distribution. The probability P(X > 18) is the sum of the probabilities for all x > 18, so we add the probabilities for x=20, x=24, and x=27, giving us 0.20 + 0.17 + 0.16 = 0.53. The probability P(X ≤ 18) includes x=18 and any values less than 18. As 18 is the lowest value given, P(X ≤ 18) is just P(18), or 0.25.
The mean μ of X is the expected value of X, computed as Σ(xP(x)). That gives us (13*0.22) + (18*0.25) + (20*0.20) + (24*0.17) + (27*0.16) = 2.86 + 4.5 + 4 + 4.08 + 4.32 = 19.76.
The variance σ 2 of X is computed as Σ [ (x - μ)^2 * P(x) ]. That gives us [(13-19.76)^2 * 0.22] + [(18-19.76)^2 * 0.25] + [(20-19.76)^2 * 0.20] + [(24-19.76)^2 * 0.17] + [(27-19.76)^2 * 0.16] = 21.61. The standard deviation σ of X is the sqrt(σ^2) = sqrt(21.61) = 4.65.
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Related Questions
In manufacturing, convenience sampling could be used to determine if the machines are operating correctly. Which of the following best describes this type of sampling?Every 10th product in the line is selectedSamples are randomly selected throughout the dayProducts are put into groups and all are included from several randomly selected groupsProducts are put into groups and some are randomly selected from each group
The cost of x game tickets if one game ticket costs 107
A line passes through A(3,7) and B(-4,9). Find the value of a if C(a, 1) is on the line.
Evaluate the expression when a= 2 and c= -7. C-4a answer
Which equation models the data in the table?
y = 6 sine (StartFraction pi Over 6 EndFraction x) + 2
y = 6 sine (StartFraction pi Over 6 EndFraction x) + 4
y = 4 sine (StartFraction pi Over 6 EndFraction x) + 6
y = 4 sine (StartFraction pi Over 6 EndFraction x) + 10
Answers
Modeling the data in the table is done via the equation y = 4 sine (pi/6x) + 6.
What is a cyclic pattern?
Over a period of years, a cyclical pattern recurs with considerable regularity. Cyclical patterns are distinct from seasonal patterns in that they last across a number of years as opposed to only one year for seasonal trends.
Given, The table shows the height of water in feet at different times. The water rises and falls in a cyclical pattern.
Table:
12 AM 6
3 AM 10
6 AM 6
9 AM 2
12 PM 6
from the general formula of wave
y = A sin(bx + c)
Substituting values in the equation from the graph attached below:
6 = A sin(0*b + c)......(1)
10 = A sin3b + c...(2)
6 = A sin6b + c......(3)
2 = A sin9b +c........(4)
Since -c/b is a phase shift of the graph
Thus
-c/b = 6
c = -6b
from equations 2 and 1
2* 6 = Asin(-3b) = -Asin3b
2 * 6 = Asin(-6b) = -Asin6b
2* 6/6 =sin6b/sin3b
1 = Cos3b
Thus b = π/6
from substitution in equations 3
6 = A sin6b + c
=> 6 = Asin 6* pi/6 + c
=> c = 6
from substitution in equations 2
10 = A sin3b + c
A = 4
therefore, The equation that models data in the table is y = 4 sine (pi/6x) + 6.
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Answer:
c
Step-by-step explanation:
Answers
i thing the answer is D the last chart
Answers
Answer:
38°
Step-by-step explanation:
<ABD and <DBC are two interior angles that make up <ABC.
Based on the Angle Addition Theorem, the following equation can be used to find m<DBC:
Find x
We are given that, m<DBC = (6x - 16)°
Plug in the value of x to find the measure
m<DBC = 6(9) - 16 = 54 - 16 = 38°
Answers
Answer:
The probability is
Step-by-step explanation:
From the question we are told that
Th The population mean
The standard deviation is
The values considered is
Given that the distribution of the amounts spent follows the normal distribution then the percent of the adults spend more than $2,550 per year on reading and entertainment is mathematically represented as
Generally
So
substituting values
From the normal distribution table the value of is
Thus
Final answer:
We calculate the z-score for the amount $2,550 using the given mean and standard deviation. The z-table gives us the percentage of people who spend less than this, which we subtract from 1 to find the percentage who spend more. Approximately 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.
Explanation:
To compute the percentage of adults spending more than $2,550 per year, we must first find the z-score associated with this value. The z-score is a measurement of how many standard deviations a particular data point is from the mean.
The formula for calculating the z-score is: Z = (X - μ) / σ.
Where:
- X is the value we are interested in.
- μ is the mean.
- σ is the standard deviation.
Using this formula, the z-score for $2,550 is:
Z = ($2,550 - $1,999) / $574 = 0.96.
Next, we need to use a z-table or a standard normal distribution table to find out the probability that lies below the calculated z-score. Looking this up on a z-table, we get a value of 0.8315, meaning that 83.15% of the population will spend $2,550 or less per year on reading and entertainment. Since we want to know the percentage spending more than $2,550, we subtract this value from 1: 1 - 0.8315 = 0.1685.
Therefore, based on the given mean and standard deviation, about 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.
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Answers
Answer:
a. $849.45
Step-by-step explanation:
In the above question, we are given the following information
Coupon rate = 10%
Face value = 1000
Maturity = n = 20 years
t = number of periods = compounded semi annually = 2
Percent yield = 12% = 0.12
Bond Value formula =
C/t × ([1 -( 1/ 1 + r/t)-^nt ÷] r/t) +( F/ (1 + r/t)^nt)
C = coupon rate × face value = 10% × 1000 = 100
Bond value:
= 100/2 × ( [1 - (1 /1 + 0.12/2)^-20×2]÷ 0.12/2)+ (1000/( 1 + 0.12/2)^20×2
= 50 × ( [1 - (1 /1 + 0.06) ^40] ÷ 0.06) + ( 1000/ (1 + 0.06) ^40
= 50 × ( [1 - (1/ (1.06) ^40] ÷ 0.06 ) + (1000/(1.06)^40)
= 50 × 15.046296872 + 97.222187709
= $849.45
Bond value = $849.45
Answers
Answer:
169 cm
Step-by-step explanation:
Mean is the average of a group of numbers. You calculate it by adding all your numbers and dividing by how many numbers you have. In this question you would solve with these steps...
Add all of your numbers
165 + 175 + 176 + 159 + 170 = 845
Divide your solution by the number of numbers you have
845 / 5 = 169
The mean of the heights of the five students is 169cm.
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