Consider the following probability distribution function of the random variable X which represents the number of people in a group (party) at a restaurant: X P(X) 1 0.10 2 0.25 3 0.20 4 0.20 5 0.10 6 7 0.05 8 0.05 a. Find the population mean of X. b. Find the population variance and standard deviation of X. c. Find the probability that the next party will be over 4 people. d. Find the probability that the next three parties (assuming independence) will each be over 4 people.
Answers
Answer:
(a) 3.55
(b) 3.45 and 1.86
(c) 0.25
(d) 0.016
Step-by-step explanation:
The random variable X denotes the number of people in a group (party) at a restaurant.
(a)
The formula to compute the mean is:
\(\mu=\sum {x\cdot P(X=x)}\)
Consider the Excel sheet attached.
The mean is, 3.55.
(b)
The formula to compute the variance is:
\(\sigma^{2}=[\sum {x^{2}\cdot P(X=x)}]-(\mu)^{2}\)
Consider the Excel sheet attached.
Compute the variance as follows:
\(\sigma^{2}=[\sum {x^{2}\cdot P(X=x)}]-(\mu)^{2}\\\\=16.05-(3.55)^{2}\\\\=3.4475\\\\\approx 3.45\)
The variance is, 3.45.
Compute the standard deviation as follows:
\(\sigma=\sqrt{\sigma^{2}}\\\\=\sqrt{3.45}\\\\=1.85742\\\\\approx 1.86\)
The standard deviation is, 1.86.
(c)
Compute the probability that the next party will be over 4 people as follows:
\(P(X>4)=P(X=5)+P(X=6)+P(X=7)+P(X=8)\\\\=0.10+0.05+0.05+0.05\\\\=0.25\)
Thus, the probability that the next party will be over 4 people is 0.25.
(d)
Compute the probability that the next three parties will each be over 4 people as follows:
It is provided that the three parties are independent.
P (Next 3 parties will be each over 4) = [P (X > 4)]³
\(=(0.25)^{3}\\=0.015625\\\approx 0.016\)
Thus, the probability that the next three parties will each be over 4 people is 0.016.
Related Questions
jack popped some popcorn, but 3 of the 150 kernels did not pop
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GUYS PLEASE ASAP I WILL FAIL IF U GUYS DONT ANSWER PLEASE
WHICH ONE IS INCORRECT
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Answer:
The table
Step-by-step explanation:
The puppy weighs 0.8 pounds at birth not 0
PLEASE HELP
y = 4x-9
y=x-3
Your work using substitution
Answers
Answer:
-36
-3y
Step-by-step explanation:
F
Answer:
(4,-7)
Step-by-step explanation:
y=4x-9
y+3=x
y=4(y+3)-9
y=4y+12+9
y=4y+21
y-4y=21
-3y=21
y=-7
Now use y to find x
y+3=x
-7+3=4
x=4
Match the terms associated with a study.
1. A summary about the group of units data is recorded on
2. A summary measure about the overall group of interest
3. The group of units data is recorded on
4. The overall group of interest
a. Population
b. Prediction
c. Inference
d. Sample
e. Parameter
f. Statistic
Answers
Using the concept of statistic, the appropriate terms associated with the study are :
1 - statistic2 - Parameter3 - Sample 4 - PopulationThe population refers to the overall group which is of interest or relevance to a particular study.
The group of unit data which is usually a subset of the population is called the sample.
A summary or measure made from the population or overall group is called the Parameter.
A summary or measure made from the group of unit data or sample is called the statistic.
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When Ibuprofen is given for fever to
children 6 months of age up to 2 years, the
usual dose is 5 milligrams (mg) per kilogram
(kg) of body weight when the fever is under
102.5 degrees Fahrenheit. How much
medicine would be usual dose for a 18
month old weighing 21 pounds?
milligrams
Round your answer to the nearest milligram.
Answers
Answer: The usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen.
Step-by-step explanation: To find the usual dose of ibuprofen for a child, we need to follow these steps:
Convert the child’s weight from pounds to kilograms. One pound is equal to 0.4536 kilograms, so we multiply 21 by 0.4536 to get 9.5256 kilograms.Multiply the child’s weight in kilograms by the dose per kilogram. The dose per kilogram is 5 mg when the fever is under 102.5 degrees Fahrenheit, so we multiply 9.5256 by 5 to get 47.628 mg.Round the result to the nearest milligram. To round a number to the nearest milligram, we look at the digit after the decimal point. If it is 5 or more, we add one to the digit before the decimal point and drop the rest. If it is less than 5, we keep the digit before the decimal point and drop the rest. In this case, the digit after the decimal point is 6, which is more than 5, so we add one to the digit before the decimal point and drop the rest. The result is 48 mg.Therefore, the usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen. Hope this helps, and have a great day! =)
3, 12, 27, 64, 75, 108
a) give the next number in this pattern
b) what is the rule to find the nth term?
c) what is the 20th term?
Please help + explain!
Answers
The third term from the sequence should be 48 so that (a) the next term is 147 (b) the rule to find the nth term is 3×n² and (c) the 20th term is 1200.
How to find the next term of the sequenceFrom the question, 3, 12, 27, 64, 75, 108 the third term 64 is supposed to be 48. hence the terms are derived as follows:
1st term; 3 × 1² = 3
2nd term;3 × 2² = 12
3rd term; 3 × 3² = 27
4th term; 3 × 4² = 48
5th term; 3 × 5² = 75
6th term; 3 × 6² = 108
Therefore, the next term which the 7th term is 3 × 7² = 147, the rule for the sequence is 3×n² and the 20th term is 3 × 20² = 1200.
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Ms. Keenan is a high school teacher who wants to know how much time students spend studying each day. She finds that the average student spends 3.00 hours a day studying (s - 0.75). Assuming that studying hours is normally distributed, what percentage of students study less than 2.50 hours a day?
© 25.14 percent
© 19.15 percent
© 10.93 percent
© 24.86 percent
Answers
The requried, percentage of students who study less than 2.50 hours a day is approximately 25.14 percent.
What is the Z -a score?A Z-score is stated as the fractional model of data point to the mean using standard deviations.
We need to convert 2.50 hours to a standard score (z-score) using the formula,
z = (x - μ) / σ
where x is the value we want to convert, μ is the mean, and σ is the standard deviation.
z = (2.50 - 3.00) / 0.75
z = -0.67
This means that 2.50 hours is 0.67 standard deviations below the mean.
We can use a standard normal distribution table or a calculator to find the percentage of the distribution that falls below this standard score. For example, using a standard normal distribution table, we can look up the area to the left of z = -0.67 and get:
P(z < -0.67) = 0.2514
So the correct answer is (a) 25.14 percent.
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A rectangular movie screen has side lengths of 7 meters and 9 meters. The size of a screen is determined by its diagonal. Of the choices given below what is the approximate for the size of the screen ?
11 meters
16 meters
63 meters
130 meters
Answers
Explanation= i plugged it into a calculator
I had that question
Good luck :)
Explain how you can find the y-intercept of a function when given an equation of a graph.
Answers
The y-intercept of a function is the value of y when x = 0, which is represented as the value of b in the slope-intercept equation y = mx + b. b is the y-intercept.
What is the Y-intercept of a Function?If an equation of graph that represents a function is given in slope-intercept form as y = mx + b, the value of b in the function is the value of the y-intercept of the y-intercept.
The y-intercept of the function is the same as the value of y when the value of x is 0, or the point where the line of the function intercepts the y-axis on a given graph that represents the function.
For example, if we are given the equation of a graph that represents a function as, y = 3x + 4, the y-intercept of the function would be 4.
In summary, the y-intercept of the function is the value of b in the equation of the function that is expressed as y = mx + b in slope-intercept form.
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Suppose that the sample size had been 4500 rather than 1033. Find the margin of error for 95% confidence for the larger sample Give your answer to three decimal places. margin of error:
Answers
The formula for calculating margin of error is expressed as
\(\text{margin of error = z }\times\text{ (}\sqrt[]{\frac{pq}{n}})\)Where
p represents the probability of success
q represents the probability of failure
n represents sample size
z represents the z score for a 95% confidence interval
From the information given,
p = 30% = 30/100 = 0.3
q = 1 - p = 1 - 0.3 = 0.7
n = 4500
From the standard normal distribution table, z = 1.96
By substituting these values into the formula, we have
\(\text{margin of error = 1.96}\times\sqrt[]{\frac{0.3\times0.7}{4500}}\text{ = }0.013\)margin of error = 0.013
John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.50 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 500 units of vitamins, 600 units of minerals, and 1200 calories. How many boxes of each cereal should he buy to minimize his cost?
Answers
Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:
10x + 5y ≥ 500 (minimum 500 units of vitamins)
5x + 10y ≥ 600 (minimum 600 units of minerals)
15x + 15y ≥ 1200 (minimum 1200 calories)
We want to minimize the cost, which is given by:
0.5x + 0.4y
This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:
10x + 5y = 500
5x + 10y = 600
15x + 15y = 1200
Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.
Next, we can calculate the value of the cost function at each corner point of the feasible region:
Corner point A: (20, 40) -> Cost = 20
Corner point B: (40, 25) -> Cost = 25
Corner point C: (60, 0) -> Cost = 30
Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.
Solve the system of equations
x+y=15
Y=x^(2)-5
(-5,20) and (4,11)
(3,4) and (7,8)
(5,10) and (-4,19)
(5,20) and (4,11)
Answers
Answer:
(a) (-5,20) and (4,11)
Step-by-step explanation:
You want the solutions to the system of equations ...
x + y = 15y = x² - 5SubstitutionUsing the second equation to substitute for y in the firs equation, we have ...
x +x² -5 = 15
x² +x -20 = 0 . . . . . subtract 15, put in standard form
(x +5)(x -4) = 0 . . . . . factor
Zero product ruleA product is zero only when one or more factors is zero. The values of x that make the factors zero are ...
x = -5 and x = 4
The corresponding values of y are ...
y = 15 -x
y = 15 -{-5, 4} = {20, 11}
The solutions are (x, y) = (-5, 20) and (4, 11).
Translate this sentence into an equation.
The product of 3 and Vidya's height is 54.
Use the variable v to represent Vidya's height.
Answers
Th equation is \(3v=54\\\).
Given,
product of 3 and vidya's height is 54
v is represented as vidya's height.
Representation of equation is as follows:
The product of 3 and vidya's height can be written as \(3*v=3v\)
and their product is 54,
\(3v=54\).
Thus, the equation is \(3v=54\\\).
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a boat is tied to a dock using 2 ropes. what is the length of rope A?
Answers
can someone please help
Answers
Answer:
The measure of CD is 46
Step-by-step explanation:
From the midpoint theorem, we have,
FG = (1/2)CD
so,
\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)
Now,
\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)
In using quarterly time series data, which quarter can serve as the base period for interpretation of dummy variables?
A. Any of the above.
B. Quarter two
C. Quarter one
D. Quarter four
E. Quarter three
Answers
In using quarterly time series data, Quarter two can serve as the base period for interpretation of dummy variables.
What do you mean by interpretation?
The process of interpreting anything involves elaborating, rephrasing, or otherwise demonstrating your own understanding of it.
Because they are explaining what someone is saying to someone who doesn't understand, a person who translates one language into another is known as an interpreter.
What are examples and variables?
A trait that is measurable and capable of taking on several values is known as a variable. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling.
The two primary categories of variables are categorical and numeric.
Learn more about variable
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If EG=71 , find the value of x
Answers
Answer:
A
Step-by-step explanation:
A = 71 so then EG = 91
Bob has $70,000 in a savings account that earns 11% annually. The interest is not compounded. How much interest will he earn in 9 months?
Answers
Answer:
139300
Step-by-step explanation:
According to the income section shown below from the 1040EZ form, if a
taxpayer filing her federal income tax return using the Single filing status
enters $8900 on line 4 for adjusted gross income, what would she enter on
line 6 for her taxable income? Assume that nobody can claim the taxpayer as
a dependent.
Answers
Answer:
The correct answer is $0
Step-by-step explanation:
The taxable income (line 6) on the 1040EZ form is:
Taxable Income = -$3,650.
If the result is negative, it means the taxpayer's income is below the standard deduction threshold, and her taxable income would be $0.
Here,
To calculate the taxable income (line 6) on the 1040EZ form, we need to subtract the standard deduction from the adjusted gross income (AGI).
For the tax year 2021 (the last available information before my knowledge cutoff in September 2021), the standard deduction for a taxpayer filing as Single is $12,550.
Given that the taxpayer's adjusted gross income (AGI) is $8,900, we calculate the taxable income as follows:
Taxable Income = AGI - Standard Deduction
Taxable Income = $8,900 - $12,550
Taxable Income = -$3,650
If the result is negative, it means the taxpayer's income is below the standard deduction threshold, and her taxable income would be $0.
The taxpayer would not owe any federal income tax in this case.
However, she may still want to file her tax return to claim any potential tax credits or receive a refund if she had taxes withheld from her paycheck during the year.
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Find the volume of the three dimensional figure in terms of x
Answers
Answer:
\(V=6x^3+3x^2\)
Step-by-step explanation:
The given figure shows a cuboid whose length is (2x+1) breadth is x and height is 3x.
We need to find the volume of the three dimensional figure.
The volume of a cuboid is given by :
V = lbh
Substitute all the values,
\(V=(2x+1)\times x\times 3x\\\\V=(2x+1)\times 3x^2\\\\= 3x^2(2x)+3x^2\\\\V=6x^3+3x^2\)
So, the volume of the figure is equal to \(6x^3+3x^2\).
Consider the two triangles. How can the triangles be proven similar by the SSS similarity theorem?
Answers
Answer:if their corresponding sides are proportional.
Step-by-step explanation:
the shortest side of a right triangle measures 7m. The lengths of the other two sides are Consecutive integers. What is the length of the other two sides?
Answers
The lengths of the other two sides of the right triangle are 24m and 25m, respectively.
Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Using this theorem, we have the equation:
\(7^2 + x^2 = (x + 1)^2\)
Expanding and simplifying this equation, we get:
\(49 + x^2 = x^2 + 2x + 1\)
Now, we can cancel out \(x^2\) from both sides of the equation:
49 = 2x + 1
Next, we can isolate 2x:
2x = 49 - 1
2x = 48
Dividing both sides by 2, we find:
x = 24
Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.
Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.
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Lashonda is saving money to buy a game. So far she has saved $6, which is two-thirds of the total cost of the game. How much does the game cost?
Answers
Answer:
The game costs $9
Step-by-step explanation:
I wrote an equation using the variable "t" for the total cost of the game.
6=2/3t
t=6/2/3
t=(6/1)(3/2)
t=18/2
t=9
Which expression represents a cube root of 1 + i?
OVE (cos()+ i sin (24))
OVE (cos (37) + i sin (3))
/
O & (cos (4) + i sin (24))
V2 (cos (37) + 1 sin (37))
Answers
Answer:c
Step-by-step explanation is va cuz when your multiply:
Answer:
\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)
Step-by-step explanation:
The analysis is as attached below.
-7(1+9a) have no idea how to do this
Answers
Answer:
-7-63a
Step-by-step explanation:
-7(1 + 9a)
(use the distributive property of multiplication to simplify)
-7-63a
How many commutes are exactly 68 minutes
Answers
Answer:
three
Step-by-step explanation:
stem. is the tens place and the leaf is the. ones place
so you want to find 68 so you look in the stem column and look for six
in the row there are 6 numbers which mean:
60, 61, 67, 68, 68, 68
as you can see there is three 68 there for the answer ths 3
What is 4 & 1/2+1/8? *
Answers
Answer:
4 5/8
Step-by-step explanation:
Rewriting our equation with parts separated
=4+12+18
Solving the fraction parts
12+18=?
Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.
LCD = 8
48+18=58
Combining the whole and fraction parts
4+58=458
Need answers asap please
Answers
The inverse of a function is n(a) = (a+30)/3 option (A) is correct by using the concept of the inverse of a function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
a(n) = 3n - 30
To find make subject n and solve
a(n) + 30 = 3n
\(\rm n = \dfrac{a(n) + 30}{3}\)
Plug n = n(a) and a(n) = a
\(\rm n(a) = \dfrac{a + 30}{3}\)
Thus, the inverse of a function is n(a) = (a+30)/3 option (A) is correct by using the concept of the inverse of a function.
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Review the graph of function f(x), which is defined for –4 < x ≤ 2.
On a coordinate plane, a curve starts at open circle (negative 4, 5), curves down to (negative 2, negative 4), and then curves up through (0, negative 1) to closed circle (2, 2).
Which table identifies the left-hand and right-hand limits at the endpoints?
Answers
Answer:
3rd option
Step-by-step explanation:
edge
Answer:
I just took the test and the answer is c
Step-by-step explanation:
Jessica wrote the equation 440xh= 3,168, where h is the same number of hours it took a jet flying at a constant speed of 440 miles per hour to travel 3,168 miles. Solve for h.
Answers
Answer:
7.1 (I rounded this number to the tenths)
Step-by-step explanation:
440÷3,168 or use long division