Using the normal distribution, it is found that:
a) 0.8599 = 85.99% probability that x is more than 60.
b) 0.1788 = 17.88% probability that x is less than 110.
c) 0.6811 = 68.11% probability that x is between 60 and 110.
d) 0.0643 = 6.43% probability that x is greater than 125.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It 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, which is the percentile of X.In this problem:
The mean is of 87, thus [tex]\mu = 87[/tex].The standard deviation is of 25, thus [tex]\sigma = 25[/tex].Item a:
This probability is 1 subtracted by the p-value of Z when X = 60, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 87}{25}[/tex]
[tex]Z = -1.08[/tex]
[tex]Z = -1.08[/tex] has a p-value of 0.1401.
1 - 0.1401 = 0.8599
0.8599 = 85.99% probability that x is more than 60.
Item b:
This probability is the p-value of Z when X = 110, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 87}{25}[/tex]
[tex]Z = 0.92[/tex]
[tex]Z = 0.92[/tex] has a p-value of 0.8212.
1 - 0.8212 = 0.1788.
0.1788 = 17.88% probability that x is less than 110.
Item c:
This probability is the p-value of Z when X = 110 subtracted by the p-value of Z when X = 60.
From the previous two items, 0.8212 - 0.1401 = 0.6811.
0.6811 = 68.11% probability that x is between 60 and 110.
Item d:
This probability is 1 subtracted by the p-value of Z when X = 125, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{125 - 87}{25}[/tex]
[tex]Z = 1.52[/tex]
[tex]Z = 1.52[/tex] has a p-value of 0.9357.
1 - 0.9357 = 0.0643.
0.0643 = 6.43% probability that x is greater than 125.
A similar problem is given at https://brainly.com/question/24863330
representation of the function f(x)=-2x2+8x-6
Use the results from a survey of a simple random sample of 1176 adults. Among the 1176 respondents, 77% rated themselves as above average drivers. We want to test the
claim that
7/10 of adults rate themselves as above average drivers. Complete parts (a) through (c)
a. Identify the actual number of respondents who rated themselves as above average drivers
(Round to the nearest whole number as needed)
Using the sample data to test the hypothesis, we have that:
The actual number of respondents who rated themselves as above average drivers is 906.The p-value of the test is 0, which is less than the standard significance level of 0.05, thus we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.7.77% of the sample of 1176 adults rated themselves as above average drivers, that is:
[tex]0.77(1176) = 906[/tex].
Thus, the actual number of respondents who rated themselves as above average drivers is 906.
At the null hypothesis, we test if the proportion is [tex]\displaystyle \frac{7}{10} = 0.7[/tex], that is:
[tex]H_0: p = 0.7[/tex]
At the alternative hypothesis, we test if the proportion is greater than 70%, that is:
[tex]H_1: p \geq 0.7[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested.n is the size of the sample.In this problem, the parameters are [tex]\overline{p} = 0.77, p = 0.7, n = 1176[/tex].
Thus, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.77 - 0.7}{\sqrt{\frac{0.7(0.3)}{1176}}}[/tex]
[tex]z = 5.24[/tex]
The p-value of the test is the probability of finding a sample proportion above 0.77, which is 1 subtracted by the p-value of z = 5.24.
Looking at the z-table, z = 5.24 has a p-value of 1.
1 - 1 = 0.
The p-value of the test is 0, which is less than the standard significance level of 0.05, thus we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.7.
A similar problem is given at https://brainly.com/question/24330815
please ans very easy question
Answer:
what is the question please tell me on comment
Can someone please show a piece of paper or ex’s plum how you do h point?
Answer:
(-1,-1)
Step-by-step explanation:
well a square has four sides and they are all equal so it would have to be (-1,-1) for the sides to be equal
PLZ HELP ME SOMEONE!!!
Answer:
131
Step-by-step explanation:
Hope this helps
Answer:
the answer is 130.9 round it up and you get 131
Step-by-step explanation:
Which function is the inverse of the function f(x) = 4x2 + 10, if the domain of f(x) is x 2 0?
Step-by-step explanation:
inverse = √((x-10)/4)
that is the answer
Answer:
Step-by-step explanation:
Please helppppppppppppp!!!!!!!!!!!!!!!!!!!!
Answer:
558
Step-by-step explanation:
The sum of the first n numbers is ½n(n + 1)
which is the left most number in each row number n
so finding the row containing 526
½n(n + 1) > 526
½n² + ½n > 526
n² + n > 1052
n² + n - 1052 > 0
n > (-1 + √(1² - 4(1)(-1052))) / 2(1)
n > 31.938
so 526 is almost to the end of the 32 row.
The end of that row is ½(32(33)) = 528
so 526 resides two spaces to the right of 528
The end of the row below it, row 33, is ½(33)(34) = 561
As each row is one number longer than the previous row, we count back
2 + 1 = 3 numbers from the end to find what is under 526
561 - 3 = 558
Based on your equation, what was the car’s approximate initial velocity (at time=0)?
From the intercept of the line of best-fit, the car’s approximate initial velocity was of 5.7 m/s.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.
For this problem, the input and the output are defined as follows:
Input: Time in seconds.Output: Velocity in m/s.Hence the points are given by:
(2, 13.1), (4, 19.8), (6, 28.1), (8, 34.6).
Using these points and a calculator, the equation is:
v = 3.64s + 5.7
The intercept of 5.7 represents the initial velocity in m/s.
A similar problem, also involving a line of best-fit, is given at https://brainly.com/question/22992800
#SPJ1
The container that holds the water for the football team is 2/3
full. After pouring out 3
gallons of water, it is 1/2
full. How many gallons can the container hold?
Answer:
18 gallons
Step-by-step explanation:
We'll find out how much of the total container was lost when pouring out by subtracting 2/3 from 1/2.
2/3 = 4/6
1/2 = 3/6
4/6 - 3/6 = 1/6
1/6 of the total amount the container could hold was lost when 3 gallons was poured out. This means that 1/6 of the container equals to 3 gallons. We can then simply multiply 3 by 6 to find the number of gallons of liquid the container can hold.
3 * 6 = 18 gallons
Checking my answer:
18 * 2/3 = 6 * 2 = 12
12 - 3 = 9
1/2 of 18 = 9
This means that our answer is correct.
In a class of 40 students, 14 students wore blue jeans.
-Write the ratio cf students wearing blue jeans to those not wearing blue jeans.
Answer: 14:26
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
Caleb wants to rent a kayak. Kayak rentals cost $91.61 for a half hour. If Caleb rents a kayak for 2.9 hours, how much will it cost him?
Answer:
$265.669
Step-by-step explanation:
$91.61 times 2.9 equals 265.669, therefore it would cost him $265.669. Round up/down if needed.
express the f.f as fraction
0.454545
Answer: 5/11
Step-by-step explanation:
Two angles are complementary. One angle is 8º less than three times the other angle. Find the measures of the angles.
Part 1 of 2
The smaller angle is
Part: 1 / 2
Part 2 of 2
The larger angle is
Submit Assignment
Answer:
Step-by-step explanation:
complementary angles sum to 90°
Let angle 1 = x
angle 2 = 3x - 8
3x - 8 + x = 90
4x = 98
x = 24.5°
3(24.5) - 8 = 65.5°
or
90 - 24.5 = 65.5°
the general solution of the equation cos3x +cos2x =sin3x/2 + Sinx/2 is
Answer:
I am doiiiiiiinnnnggg just wait
Hello, i need some help for questions 2-5 please
Answers:
4. =9.999........
Examplantion :
5×2÷3=9.99999..........
PLZ ANSWER WILL GIVE BRAINLYEST!!!!
What are the x and y-intercepts of the line described by the equation?
3x−9y=10.8
Question 2 options:
x-intercept = 1.2
y-intercept = -3.6
x-intercept = -1.2
y-intercept = 3.6
x-intercept = -3.6
y-intercept = 1.2
x-intercept = 3.6
y-intercept = -1.2
Answer:
x-intercept = 3.6
y-intercept = -1.2
Step-by-step explanation:
HELPS! TYS IF U DOESSSSS
I WILL GIVE BRAINILEST!!!!!!!!!
Answer:
C. HI my other account:P
Step-by-step explanation:
Help please i just wanna pass
When the mortgage is completely paid off your house, it will be 5 times as old as it is now. If you have 28 years left on the mortgage, how old is the house now?
help meeeeeeeeeeeee
2/3u. 4/2u².3=
Answer:
4u³
Step-by-step explanation:
2/3u × 4/2u² = 4/3u³
4/3u³ × 3/1 = 4u³
Answer:
4u³Step-by-step explanation:
[tex]2/3u*4/3u^2*3=[/tex][tex]2/3*4/2*3u^{1+2}=[/tex][tex]4u^3[/tex]PLS HELP ME I NEED IT
Step-by-step explanation:
the area = [tex](\frac{1}{2}) (18)(4)\\[/tex] = [tex]36ft^{2}[/tex]
please give me a brainliest answer
3 ice cream cones cost $ 8.25
At this rate , how much do 2 ice cream cones cost ?
Answer:
The cost of 2 icecream cones is $5.50. Given data: Price of 3 icecream cones is $8.25. 1 icecream come = $(8.25÷3) =$ 2.75.
Step-by-step explanation:
Answer:
5.50
Step-by-step explanation:
8.25 divided by 3 =2.75
Then take 2.75 and multiply it by 2 and you get your answer which is 5.50
como se escribe 654,007,000 en letra
Answer:
seiscientos cincuenta y cuatro millones siete mil
The perimeter of a rectangle downtown courtyard is 174 feet. The width of the rectangle is twice the length. Find the length and width of the rectangle?
Answer:
Step-by-step explanation:
L = Length
W = Width
W = 2L
2W + 2L = 174
2(2L) + 2L = 174
6L = 174
L = 29 ft
W = 2(29) = 58 ft
Use rounding to the nearest whole number to estimate the product
4 1/4 • 7 9/17
A) About 32
B) About 35
C) About 40
D) About 25
Answer:
A) About 32Step-by-step explanation:
4 1/4 • 7 9/17The first one is rounded down as 1/4 < 1/2 and the second one rounded up as 9/17 > 1/2.
4 * 8 = 32Correct choice is A
Product
17/4(128/17)128/432Option A
Justine has 4 1/2 pounds of red apples, 3 1/4 pounds of green apples, and 2 1/4 pounds of yellow apples. How many kilograms of apples does she have?
From past experience, it is known that a telemarketer makes a sale with probability 0.2. Assuming that results from one call to the next are independent. Determine the probability that telemarketer makes:___.
a. the first sale on the third call
b. the first sale after the third call
c. the second sale on the fifth call
d. the second sale before the fifth call
The area of manang district is square kilometre is 2,246 find the prime factors of 2246
What did James earn this pay period? (use pay stub) *
1 point
$1451.28
$1000.00
$709.74
Help please thank you