9514 1404 393
Answer:
(x, y, z) = (20, 4, 5)
Step-by-step explanation:
The last two equations allow y and z to be expressed in terms of x, so we have ...
3x +2(5y) -3(4z) = 40
3x +2(x) -3(x) = 40
x = 20 . . . . . . . . . . . . divide by the coefficient of x
y = 20/5 = 4
z = 20/4 = 5
The solution is (x, y, z) = (20, 4, 5).
A cheeseburger franchise uses 11 different buns, 4 different cheeses, 3 types of lettuce, and 4 types of tomatoes. Takes 10 minutes to eat each cheeseburger. How long will it take to eat all of the possible cheeseburgers
Answer:
2.2
Step-by-step explanation:
It would take 15840 min to eat all of them that means 264 hours or 11 days
lol why you need this info?
Last month, Ginger's hotel ran an occupancy rate of 85%. Her competitive set had 150,000 room nights included within it that were available for sale during that month. During that month, the competitive set sold a total of 115,000 rooms. What was the approximate occupancy rate INDEX last month for Ginger's hotel? Group of answer choices
Answer:
111
Step-by-step explanation:
-The occupancy rate index is calculated using the following formula:
[tex]Index=\frac{Hotel \ OCC}{Competitive \ OCC}\times 100[/tex]
-The Hotel OCC is the property's occupancy rate given as 85%
-The Competitive OCC, is the competitive set's occupancy rate calculated as;
[tex]Occupancy \ Rate=\frac{Room \ Sold}{Rooms \ Available}\\\\\\=\frac{115000}{150000}\\\\=76.67\%[/tex]
-We then substitute to solve for the occupancy rate index:
[tex]Index=\frac{Hotel \ OCC}{Competitive \ OCC}\times 100\\\\=\frac{0.85}{0.7767}\times 100\\\\=110.86\\\approx 111[/tex]
Hence, the occupancy rate index is 111
Find the savings plan balance after 18 months with an APR of 2% and monthly payments of $200.
The balance is $ 1
(Do not round until the final answer. Then round to the nearest cent as needed.)
Answer:
$800 [((1.005)18 - 1)/.005]
$800 x [(1.0939 - 1)/.005]
$800 x (0.0939/0.005)
$800 x 18.785
~ $15,028
The savings plan is 15,028.
Step-by-step explanation:
The savings plan balance on the account after 18 months is $3651.46.
What is the balance after 18 months?Basically, the savings plan balance means the total amount of money saved and accumulated in a designated account or investment over a period of time.
The savings plan balance will be found using annuity formula [tex]P * [(1 + r)^n - 1] / r[/tex]
Data:
P = Monthly payment = $200r = Monthly interest rate = 0.02 / 12 = 0.00166667n = Number of months = 18The plan balance will be:
= 200 * [(1 + 0.00166667)^18 - 1] / 0.00166667
= 200 * 18.2572814188
= 3651.45628376
= 3651.46.
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Helena is in charge of selling tickets for the upcoming
play at Willowbrook School. Each drama club member
has been asked to sell tickets to friends and family
members, and Helena wants to know approximately how
many tickets have been sold so far.
Homeroom Data of Tickets Sold:
20, 15, 19, 16, 10
Calculate the mean
Answer:
16
Step-by-step explanation:
You want the mean of {20, 15, 19, 16, 10}.
MeanThe mean is the sum of the numbers, divided by the number of numbers.
(20 +15 +19 +16 +10)/5 = 80/5 = 16
The mean is 16.
Final answer:
The mean of tickets sold by Helena for the Willowbrook School play is calculated by adding the total tickets sold (80) and dividing by the number of homerooms (5), resulting in a mean of 16 tickets.
Explanation:
To calculate the mean of tickets sold for the Willowbrook School play, we need to add up the number of tickets sold in each homeroom and then divide by the number of homerooms. The data given is:
20 tickets15 tickets19 tickets16 tickets10 ticketsAdding these together, we get 20 + 15 + 19 + 16 + 10 = 80 tickets sold in total. As there are 5 sets of data, we divide the total by 5 to find the mean.
Therefore, the mean number of tickets sold is 16 tickets.
Shaun needs to make mortar for brick-laying. It is made in the ratio 7:3 of sand to cement.
If 210 kg of sand is used, how much cement is needed?
You select a marble without looking and then put it back. If you do this 60 times, what is the best prediction possible for the number of times you will pick a blue or a purple marble?
The best prediction for selecting a blue marble 60 times, with replacement, from a bag of 4 blue marbles and 3 white marbles is approximately 34.29 times.
To predict the number of times you will select a blue or purple marble, we need to know the total number of marbles, the number of blue marbles, the number of purple marbles, and the number of trials (which is 60 in this case). Since no information about purple marbles is provided, let's assume you meant blue marbles only for this explanation. In the scenario presented in the question, the probability of drawing a blue marble is 4/7 each time since there are 4 blue marbles and 3 white marbles, totaling 7 marbles.
The probability of drawing a blue marble is 4/7.Each draw is independent because the marble is replaced each time.The predicted number of times a blue marble is drawn in 60 trials is calculated by multiplying the probability by the number of trials which is (4/7) * 60.Therefore, the best prediction for the number of times a blue marble will be selected is approximately 34.29 times (which you might round to 34 times).
The circular base of the cone has a radius of 5 cm. The height of the cone is 12 cm and the slant height is 13 cm. What is approximate surface area of the cone? Use 3.14 as pi and round to the nearest whole number!
Answer: 283cm
Step-by-step explanation:
You wish to determine the effectiveness of taking Omega-3 tablets to lower a person’s cholesterol. To determine this, you collect data on the cholesterol level of 50 individuals before and after a 6-week course of Omega-3 tablets. Which test would determine if this treatment was effective? a. Two-Sample t-test for means b. Two-Sample z-test for means c. Matched-Pairs t-test d. Two-Sample z-test for proportions
Answer:
Option C - Matched-Pairs t-test
Step-by-step explanation:
Looking at the options given,
-Two-Sample t-test for means is used to test the difference (d0) between two population means. A common application is to determine whether the means are equal. This can't apply to the question as it determine if this treatment was effective.
- Two-Sample z-test for means is used to test the null hypothesis that there is no difference between the means of two independent populations. This doesn't determine if this treatment was effective
-Matched-Pairs t-test is used to test whether there is a significant mean difference between two sets of paired data. This will be sufficient to determine if this treatment was effective
-Two-Sample z-test for proportions is used when we want to know whether two populations or groups (e.g., males and females; theists and atheists) differ significantly on some single (categorical) characteristic - for example, whether they are vegetarians. This can't be used to determine if this treatment was effective
The only correct option is Matched-Pairs t-test
To evaluate the effectiveness of Omega-3 tablets for lowering cholesterol, a Matched-Pairs t-test should be used, as it compares the cholesterol levels before and after treatment in the same individuals.
Explanation:To determine the effectiveness of taking Omega-3 tablets to lower a person's cholesterol, one should use a statistical hypothesis test that compares two related samples. In this case, the comparison is between cholesterol levels before and after the 6-week course. Since the same individuals are tested twice, the appropriate test is the Matched-Pairs t-test (also known as the paired sample t-test or dependent sample t-test). This test is utilized when you have two sets of related data and want to assess if their means differ. The differences between each pair will follow a normal distribution if certain conditions are met, which is assumed in a matched-pairs t-test.
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{83,73,83,59,24,12,43, 83, 59}
What is the mean, median, mode, and range for the set
Look at the attached picture⤴
Hope it will help uh...:)
Answer:
Mean: 57.667
Median: 59
Mode: 83
Range: 71
Explanation
Mean = sum of values / number of values
[tex]\frac{x1+x2...xn}{n}[/tex] = [tex]\frac{83+73+83+59+24+12+43+83+59}{9}[/tex] = 57.667Median = middle number
values sorted smallest to largest: 12, 24, 43, 59, 59, 73, 83, 83, 83 = 59Mode = number that occurs most often
There are 3 83s, so 83 is the mode = 83Range = largest number minus smallest number
83 - 12 = 71Jordan spends $9.90 for 5 pounds of apples find the unit cost 7 dollars
Answer:
$1.98/ lbs
Step-by-step explanation:
To find the unit cost, take the total cost and divide the the number of units purchased
$9.90/5 lbs
$1.98/ lbs
A certain organization recommends the use of passwords with the following format: consonant commaconsonant, consonant comma vowel comma consonant comma vowel comma consonant comma numberconsonant, vowel, consonant, vowel, consonant, number (for example, prinay 6prinay6). Assume that repeats are allowed. Complete parts (a) and (b). (a) Assuming passwords are not case sensitive, how many such passwords are possible (assume that there are 5 vowels and 21 consonants)?
Answer: (a). Passwords = 48620250
(b). Passwords = 3111696000
Step-by-step explanation:
The question reads that 'A certain organization recommends the use of passwords with the following format':
Consonant, Vowel, Consonant, Consonant, Vowel, Consonant, Number, Number (for example, pinray45).
The number of consonants is 21, the number of vowels is 5 and the numbers are 10 (0 to 9).
Since, there are 21 consonants and 5 vowels and repetition is allowed.
Use the general multiplication rule for each characters in the sequence.
Multiply by 21 consonants, 5 for vowels and 10 for numbers.
Assuming that the passwords are not case sensitive.
i.e. upper case & lower case letters are same.
Thus, the number of possible passwords is:
Passwords = Consonant * Vowel * Consonant * Consonant * Vowel * Consonant * Number * Number
Passwords = 5 x 21 x 21 x 21 x 5 x21 x 10 = 48620250
(b). Assuming that the passwords are case sensitive
Passwords = 10 x 42 x 42 x 42 x 10 x 42 x 10 = 42 x 420³ = 3111696000
cheers i hope this helps!!!!
The total number of possible passwords is 95,887,125,000.
Explanation:To calculate the number of possible passwords, we need to consider the number of choices for each position in the password. In the given format, we have 5 positions for consonants, 2 positions for vowels, and 1 position for a number. Let's break it down:
For the 1st consonant position, we have 21 choices (since there are 21 consonants).
For the 1st vowel position, we have 5 choices (since there are 5 vowels).
For the 2nd consonant position, we have 21 choices.
For the 2nd vowel position, we have 5 choices.
For the 3rd consonant position, we have 21 choices.
For the number position, we have 10 choices (since there are 10 numbers).
For the 4th consonant position, we have 21 choices.
For the 3rd vowel position, we have 5 choices.
For the 5th consonant position, we have 21 choices.
Finally, for the last consonant and the last vowel positions, we have 21 and 5 choices respectively.
To find the total number of possible passwords, we multiply the number of choices for each position:
Total number of passwords = 21 * 5 * 21 * 5 * 21 * 10 * 21 * 5 * 21 * 5 = 95,887,125,000.
What is x in this geometry equation?
Answer:
x = 7
Step-by-step explanation:
[tex]m\overset{\frown} {PQ} = m\overset{\frown} {MN}... (given) \\
\therefore Chord \:PQ \cong Chord\: MN\\
\therefore \: 4x + 10 = 38 \\ \therefore \: 4x= 38 - 10\\ \therefore \: 4x= 28\\ \therefore \: x= \frac{28}{4} \\ \huge \red{ \boxed{\therefore \: x= 7}}[/tex]
A researcher is interested in the lengths of brook trout, which are known to be approximately Normally distributed with mean 80 centimeters and standard deviation 5 centimeters. To help preserve brook trout populations, some regulatory standards need to be set for limiting the size of fish that can be caught. What is the probability of catching a brook trout less than 72 centimeters in length
Answer:
[tex]P(X<72)=P(\frac{X-\mu}{\sigma}<\frac{72-\mu}{\sigma})=P(Z<\frac{72-80}{5})=P(z<-1.6)[/tex]
And we can find this probability with the normal standard distirbution or excel and we got:
[tex]P(z<-1.6)=0.055[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the lenghts of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(80,5)[/tex]
Where [tex]\mu=80[/tex] and [tex]\sigma=5[/tex]
We are interested on this probability
[tex]P(X<72)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X<72)=P(\frac{X-\mu}{\sigma}<\frac{72-\mu}{\sigma})=P(Z<\frac{72-80}{5})=P(z<-1.6)[/tex]
And we can find this probability with the normal standard distirbution or excel and we got:
[tex]P(z<-1.6)=0.055[/tex]
Which statement is true
A. (X,y) (x-7,y+2) represents a translation 7 units down and 2 units to the right
B. (X,y) (-x,-y) represents a rotation 180° clockwise
C. (X,y) (x+3.5,y+3.5) represents a dilation wuth a scale factor of 3.5
D. (X,y) (-x, y) represents a reflection over the x axis
Answer:
B
Step-by-step explanation:
this is true because if you rotate 180 degrees on a graph both the x and y will always become their opposite.
Which of the following statements are correct? A. The statement that the random variable X is normally distributed with parameters is often abbreviated . B. If the random variable X is normally distributed with parameters , then . C. The graph of any normal probability density function is symmetric about the mean and bell-shaped, so the center of the bell (point of symmetry) is both the mean of the distribution and the median. D. If the random variable X is normally distributed with parameters , then a large implies that a value of X far from may well be observed, whereas such a value is quite unlikely when is small. E. All of the above statements are correct
Answer:
A. The statement that the random variable X is normally distributed with parameters is often abbreviated.
Step-by-step explanation:
The X is normally distributed with parameters u and is often distributed as X ≈N (u 2 ). The correct answer is a. The statement that the random variable is normally distributed.
what is the probability of rolling a dice twice, and having it land on a number greater than 1 both times?
Answer:
25/36
Step-by-step explanation:
P(1) = 1/6
P'(1) = 5/6
5/6 * 5/6 = 25/36
Show a number line to the inequality x-1>2
Answer:
see below
Step-by-step explanation:
x-1>2
Add 1 to each side
x-1+1>2+1
x >3
There would be an open circle at 3 and a line to the right
abby is making a maze for her pet mouse the diameter of the maze is 24 what is the circumference
Answer:
75.36
Step-by-step explanation:
To find the diameter, take the radius and multiply it by two, or use the diameter, and then multiply by pi. The formula, in this case, would be pi x 24. I hope this helps. I used 3.14, the shorter version, but a more precise answer would be 75.3982236862, or 75.4 rounded.
A waiter served 12 customers at lunch. Then he worked the dinner shift and served 5 new customers per hour. Write an equation that represents the number of customers the waiter served over lunch and dinner. Identify the x and y variables and explain the meaning of the slope and y-intercept.
The question is asking to find an equation of how many customers the waiter served.
Given: 12 customers at lunch; 5 per hour for dinner
Find: number of customers served at lunch AND dinner
We use variables for this, x and y. A general equation is usually y=ax+b, where y is the solution, x is the variable, and a and b are numbers.
Knowing this information, since it is already given that 12 customers were served, the equation turns into y=ax+12
Additionally, since we don't know how many hours she worked, we can use that as a variable. y=5x+12
x=how many hours the waiter worked at dinner
y=overall hours the waiter worked at both lunch and dinner
slope=5, means customers are going up 5 every hour
y-intercept=12, the given/starting point on the y-axis
mike is flying a kite the horizontal distance to the kite a is about 19 feet the kite is 31 feet from the ground how long is the string
Answer:36.36feet (that rounded but if you want you can round it to 36.4
Step-by-step explanation:
Final answer:
The problem involves using the Pythagorean theorem to find the length of a kite string given the horizontal and vertical distance, which would be the square root of the sum of the squares of 19 feet and 31 feet.
Explanation:
The student's question concerns the length of the string used to fly a kite when given the horizontal distance and the vertical distance from the ground to the kite. To solve this, we apply the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this problem, the kite string functions as the hypotenuse, the horizontal distance to the kite is one leg, and the vertical distance from the ground to the kite is the other leg.
For Mike's kite:
The horizontal distance (leg a) to the kite = 19 feetThe vertical distance (leg b) from the ground to the kite = 31 feetAccording to the Pythagorean theorem:
[tex]\( c^2 = a^2 + b^2 \\( c^2 = 19^2 + 31^2 \\( c^2 = 361 + 961 \\( c^2 = 1322 \\( c = \\( c \\) = \\( c \\) = \\) is the length of the kite string[/tex].
Therefore, Mike's kite string is approximately \\( c \\) long.
In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more than 92 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and non methane organic gas (NMOG) over the useful life ( 150,000 miles of driving) of the vehicle. NOX + NMOG emissions over the useful life for one car model vary Normally with mean 88 mg/mi and standard deviation 4 mg/mi. (a) What is the probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG? (Enter your answer rounded to four decimal places.)
Answer:
0.6915
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 problem, we have that:
[tex]\mu = 88, \sigma = 4[/ex]
What is the probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG?
This is 1 subtracted by the pvalue of Z when X = 86. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{86 - 88}{4}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a pvalue of 0.3085
1 - 0.3085 = 0.6915
The answer is 0.6915
A videotape store has an average weekly gross of $1,158 with a standard deviation of $120. Let x be the store's gross during a randomly selected week. If this is a normally distributed random variable, then the number of standard deviations from $1,158 to $1,360 is:
Answer:
The number of standard deviations from $1,158 to $1,360 is 1.68.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 problem, we have that:
[tex]\mu = 1158, \sigma = 120[/tex]
The number of standard deviations from $1,158 to $1,360 is:
This is Z when X = 1360. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1360 - 1158}{120}[/tex]
[tex]Z = 1.68[/tex]
The number of standard deviations from $1,158 to $1,360 is 1.68.
The function f(x) = -3x + 200 shows the height in feet of Complete the statements to show the difference in the
a feather dropped from an initial height of 200 feet above mathematical and reasonable domain and range for the
the moon's surface after x seconds.
function. Round any decimals to the nearest integer.
Mathematical range:ys
Reasonable range:
Answer:
Mathematical 200
reasonable 0,200
Step-by-step explanation:
i got it right on the test
cuantas unidades mide el lado QR? cual es la distancia entre los puntos P y R
Answer:
Part A) [tex]QR=2\sqrt{5}\ units[/tex]
Part B) [tex]PR=2\sqrt{13}\ units[/tex]
Step-by-step explanation:
The complete question in English is
Observe the isosceles PQRS trapeze in the Cartesian plane.
A) How long is the QR side?
B) What is the distance between points P and R?
The picture of the question in the attached figure
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Part A) How long is the QR side?
we have the coordinates
Q(7,6) and R(9,2)
substitute in the formula
[tex]d=\sqrt{(2-6)^{2}+(9-7)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(2)^{2}}[/tex]
[tex]d_Q_R=\sqrt{20}\ units[/tex]
simplify
[tex]d_Q_R=2\sqrt{5}\ units[/tex]
Part B) What is the distance between points P and R?
we have the coordinates
P(3,6) and R(9,2)
substitute in the formula
[tex]d=\sqrt{(2-6)^{2}+(9-3)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(6)^{2}}[/tex]
[tex]d_P_R=\sqrt{52}\ units[/tex]
simplify
[tex]d_P_R=2\sqrt{13}\ units[/tex]
What is the area of the sector that is not shaded?
Answer:
24
Step-by-step explanation:
The radius of a sphere X is 3 inches, and radius of sphere Y is 9 inches. How many
times larger is the volume of sphere Y compared to sphere X?
The volume of the sphere Y is 27 times the volume of the sphere X
Step-by-step explanation:
Sphere X:
Radius of sphere X = 3 inches
Volume = (4/3) π(27)
Sphere Y:
Radius of sphere Y = 9 inches
Volume = (4/3) π(729)
Volume of sphere Y /volume of sphere X = (4/3) π(729) /(4/3) π(27)
= (729) /(27)
= 27
The volume of the sphere Y is 27 times the volume of the sphere X
Solve 2 + 3ex + 2 = 7 for x.
Answer:
The answer is C. x=In(5/3)-2
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
3.- In a certain desert region the average number of persons who become seriously ill each year from eating a certain poisonous plant each year is 3.2, determine what is the probability that at least 5 people will become seriously ill in two years (hint: this is a rare event and can be modeled using a Poisson distribution)
Answer:
[tex]P(X\geq 5)=1-P(X<5)=1-P(X\leq 4)=1-[P(X=0)+P(X=1)+P(X=2) +P(X=3) +P(X=4)][/tex]
Using the pmf we can find the individual probabilities like this:
[tex]P(X=0)=\frac{e^{-6.4} 6.4^0}{0!}=0.001662[/tex]
[tex]P(X=1)=\frac{e^{-6.4} 6.4^1}{1!}=0.010634 [/tex]
[tex]P(X=2)=\frac{e^{-6.4} 6.4^2}{2!}=0.034029 [/tex]
[tex]P(X=3)=\frac{e^{-6.4} 6.4^3}{3!}=0.072595 [/tex]
[tex]P(X=4)=\frac{e^{-6.4} 6.4^4}{4!}=0.116151 [/tex]
And replacing we got:
[tex] P(X \geq 5) =0.76493[/tex]
Step-by-step explanation:
Previous concepts
Let X the random variable that represent the number of people that will become sereiosly ill in two years. We know that [tex]X \sim Poisson(\lambda)[/tex]
The probability mass function for the random variable is given by:
[tex]f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...[/tex]
And f(x)=0 for other case.
For this case the value for [tex]\lambda[/tex] would be:
[tex]\lambda = 3.2 \frac{ills}{year} *2 years = 6.4[/tex]
For this distribution the expected value is the same parameter [tex]\lambda[/tex]
[tex]E(X)=\mu =\lambda[/tex]
On this case we are interested on the probability of having at least two chocolate chips, and using the complement rule we have this:
[tex]P(X\geq 5)=1-P(X<5)=1-P(X\leq 4)=1-[P(X=0)+P(X=1)+P(X=2) +P(X=3) +P(X=4)][/tex]
Using the pmf we can find the individual probabilities like this:
[tex]P(X=0)=\frac{e^{-6.4} 6.4^0}{0!}=0.001662[/tex]
[tex]P(X=1)=\frac{e^{-6.4} 6.4^1}{1!}=0.010634 [/tex]
[tex]P(X=2)=\frac{e^{-6.4} 6.4^2}{2!}=0.034029 [/tex]
[tex]P(X=3)=\frac{e^{-6.4} 6.4^3}{3!}=0.072595 [/tex]
[tex]P(X=4)=\frac{e^{-6.4} 6.4^4}{4!}=0.116151 [/tex]
And replacing we got:
[tex] P(X \geq 5) =0.76493[/tex]
Answer:
The probability that at least 5 people will become seriously ill in two years is 0.7649.
Step-by-step explanation:
The question mentions that this problem can be modeled using the Poisson distribution so, we will use the formula:
P(X=x) = [(e^-λt)*(λt^x)]/x!
where λ = average number of occurrences per year
t = no. of years
x = number of people
We need to determine P(X≥5) so first we will calculate the probabilities at X=0,1,2,3,4 and subtract them from the total probability i.e. 1 to find P(X≥5).
We have λ = 3.2, t=2 years hence λt = (3.2)(2) = 6.4. So,
P(X=0) = [(e^(-6.4)*(6.4^0)]/0! = 0.00166
P(X=1) = [(e^(-6.4)*(6.4^1)]/1! = 0.01063
P(X=2) = [(e^(-6.4)*(6.4^2)]/2! = 0.03403
P(X=3) = [(e^(-6.4)*(6.4^3)]/3! = 0.07259
P(X=4) = [(e^(-6.4)*(6.4^4)]/4! = 0.011615
P(X≥5) = 1 - P(X<5)
= 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)]
= 1 - (0.00166 + 0.01063 + 0.03403 + 0.07259 + 0.011615)
= 1 - 0.23506
P(X≥5) = 0.7649
The probability that at least 5 people will become seriously ill in two years is 0.7649.
Which value of x makes x-16=32true?
Answer:
48
Step-by-step explanation:
32+16=48
48-16=32
Answer:
48
Step-by-step explanation:
add 32 and 16 to get 48
A test of H0: p = 0.5 versus Ha: p > 0.5 has the test statistic z = 1.15. Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points) Part B: If the alternative hypothesis is Ha: p ≠ 0.5, what conclusion can you draw at the 5% significance level? At the 1% significance level? (4 points)
Answer:
Part A: The null hypothesis failed to be rejected.
Part B: The null hypothesis failed to be rejected.
Step-by-step explanation:
We have an hypothesis test with null and alternative hypothesis H0: p = 0.5 versus Ha: p > 0.5, which has the test statistic z=1.15.
Part A: If the significance level is 0.05, the conclusion depends on the P-value.
If the P-value is below 5%, the null hypothesis is rejected.
The P-value for this right-tailed tes and z=1.15 is:
[tex]P-value=P(z>1.15)=0.125[/tex]
The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.
Part B: In this case, the significance level is 0.01 and, as the alternative hypothesis is defined with an unequal sign, the test is two-tailed.
This changes the way we calculate the P-value, as we need to compute the two tails.
The P-value is:
[tex]P-value=2P(z>1.15)=0.25[/tex]
The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.
Null hypothesis of a sample suggest that there is no statistical relationship exists in a set of provided single observed variable. The null hypothesis is failed to be rejected for both part A and part B of the question.
Given-Using the hypothesis test we have,
[tex]H_o; p=0.5[/tex]
[tex]H_ap>0.5[/tex]
[tex]z=1.15[/tex]
Null hypothesisNull hypothesis of a sample suggest that there is no statistical relationship exists in a set of provided single observed variable.
Part A: The conclusion to draw at the 5% significance level-
In the right tailed test or upper test the p value for the z score can be given form z table which is,
p-value[tex]=0.125[/tex]
Here the p value 0.125 is bigger than the significance level 0.05. Thus the effect is not significant and the null hypothesis is failed to be rejected.
Part B: If the alternative hypothesis is Ha: p ≠ 0.5, the conclusion to draw at the 5% significance level-
Here for the unequal sign 2-test is performed. The p value for the 2-test is,
p- value[tex]=0.25[/tex]
Here the p value 0.25 is bigger than the significance level 0.05. Thus the effect is not significant and the null hypothesis is failed to be rejected.
Hence, the null hypothesis is failed to be rejected for both part A and part B of the question.
For more about the null hypothesis, follow the link below-
https://brainly.com/question/4454077