Answer:
a) mean = 24, standard deviation = 3.098386
b) the probability of exactly 27 successes is 0.08265
c) the probability of fewer than 30 successes is 0.96478
d) the probability of more than 20 successes is 0.8702
Step-by-step explanation:
Given the data in the question,
p = 0.60
n = 40
a) mean and standard deviation;
mean = np = 40 × 0.6
mean = 24
we know that Variance = np( 1 - p )
so standard deviation S.D = √( np( 1 - p ) )
S.D = √( 40 × 0.6( 1 - 0.6 ) )
S.D = √( 24( 0.4) )
S.D = √9.6
S.D = 3.098386
standard deviation = 3.098386
b) the probability of exactly 27 successes
P( x=27 ) = ⁴⁰C₂₇ × ( 0.6 )²⁷ × ( 0.4 )⁽⁴⁰⁻²⁷⁾
= ⁴⁰C₂₇ × ( 0.6 )²⁷ × ( 0.4 )¹³
= [40! / ( 27!( 40 - 27 )! )] × ( 0.6 )²⁷ × ( 0.4 )¹³
= 0.08265
Hence, the probability of exactly 27 successes is 0.08265
c) the probability of fewer than 30 successes.
P( x < 30 ) = 1 - P( x ≥ 30 )
= 1 - 0.3522248
= 0.96478
Hence, the probability of fewer than 30 successes is 0.96478
d) the probability of more than 20 successes.
p( x > 20 ) = 1 - P( x ≤ 20 )
= 1 - 0.1297657
= 0.8702
Hence, the probability of more than 20 successes is 0.8702
Grandma Gertrude’s Chocolates, a family owned business, has an opportunity to supply its product for distribution through a large coffee house chain. However, the coffee house chain has certain specifications regarding cacao content as it wishes to advertise the health benefits (antioxidants) of the chocolate products it sells. In order to determine the mean % cacao in its dark chocolate products, quality inspectors sample 30 pieces. They find a sample mean of 4% with a standard deviation of 2%. What is the margin of error at 90% confidence?
a. 1.49%
b. 1.24%
c. 0.62%
d. 0.75%
e. 1.36%
Answer:
c. 0.62%
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 30 - 1 = 29
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 29degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.6991
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
Sample of 30, standard deviation of 2%.
Then
[tex]M = T\frac{s}{\sqrt{n}} = 1.6991\frac{2}{\sqrt{30}} = 0.62[/tex]
0.62%, so option c.
Product of [x y] [1 2] is
Answer:
12xy
Step-by-step explanation:
Product of [x y] [1 2] is
(xy)×(12)=12xy
The random variable X is normally distributed with mean of 80 and variance of 36. The 67th percentile of the distribution is
Answer:
82.64
Step-by-step explanation:
Mean = 80 ; σ² = 36 ; σ = √36 = 6
Using the relation :
P(Z < x) = (x - mean) / standard deviation
P(Z < x) = 0.67
Z = invNorm(0.67) = 0.44
Hence,
0.44 = (x - 80) / 6
Cross multiply :
6 * 0.44 = x - 80
2.64 = x - 80
2.64 + 80 = x
82.64 = x
Hence, X = 82.64
Determine whether the given description corresponds to an observational study or an experiment.
A quality control specialist compares the output from a machine with a new lubricant to the output of machines with the old lubricant.
Answer:Good luck hopefully somebody answer your question
Step-by-step explanation:
Lisa rectangular living room is 20 feet wide if the length is 6 feet less than twice the width what is the area of a living room
Answer:
Step-by-step explanation:
20 * ((2*20)-6)
20*34
680
A mountain bike is prices at $413 if the sale tax is 6.5 percent what is the cost to purchase the mountain bike ? Round to the nearest cent if necessary
The cost to purchase the mountain bike is $439.85.
ayudaaaaa por favor
Answer:
La respuesta es treinta coma seis.
Espero que esto ayude.
What is the percent change from 40 to 55? Show calculations and final answer. Round to the nearest percent.
Answer:
73%
Step-by-step explanation:
40/55 x 100
= 72.72727273
Rounded = 73%
Hope this helps!
Write the equation of the ellipse 4x^2+9y^2+72x+108y+612=0 in standard form.
Answer:
(x+9)^2 + (y+6)^2
9 4 =1
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
If you know how to solve this, Please answer it. Thank You
The first one to answer the question right, will get Brainlist!
I PROMISE!!!!!
Answer:
48
Step-by-step explanation:
x1 = 20 ; y1 = 12
x2 = ? ; y2 = 5
[tex]\frac{x_{1}}{x_{2}}=\frac{y_{2}}{y_{1}}\\\\\frac{20}{x_{2}}=\frac{5}{12}\\\\20 *12 = x_{2}*5\\\\\frac{20*12}{5}=x_{2}\\\\4*12=x_{2}\\\\x_{2}=48[/tex]
Find the slope of the line passing through the points (3,16) (8,18)
A) 2/5
B)-5/2
C)5/2
D)-2/5
Answer:
2/5
Step-by-step explanation:
Slope of line is also called the gradient of line.
The formula of gradient of a straight line is always (y1-y2)/(x1-x2)
Graph the slope Y=1/7x+1
The 1 in y = 1/7x+1, is the y-intercept. Its coordinates are (0,1). 1/7 means you are going up 1 and to the right 7, since it's positive.
On a graph, it looks like the graph above.
What is the probability of flipping a coin 8 times and getting heads 2 times? Round your answer to the nearest tenth of a percent. O A. 27.3% O B. 10.9% O C. 21.9% O D. 3.1% SUBMIT
Answer:
I have the same doubt so pls answer
Step-by-step explanation:
Answer: 10.9
Step-by-step explanation
On a map of a campground, the distance between the general store and the highway is 5 cm. If 1cm = 500m on a map, what is the actual distance in kilometers between the general store and the highway?
Answer:2500
Step-by-step explanation:5 x 500 = 2500
The perimeter of a square piece of gold is 28 millimeters. How long is each side?
Answer:
7 millimeters
Step-by-step explanation:
Perimeter is the distance around an object.
The object is a square so all sides are equal. This means that we can do 28mm / 4 and get our answer of 7 millimeters.
Aryav has 3,974 baseball cards. He wants to put them in collector sheets that hold 32 cards per sheet. How many sheets does Aryav need for his entire collection?
What can they do with the remainder?
Pls try to answer both questions.
Answer:
he will need 125 college tor sheets
3,974 / 32 =124.1875
I'm not sure about the second part its a little unclear.
Answer:
Step-by-step explanation:
3,974 / 32 = 124 R 6
I think they should give the remainder (6) away to other people or keep it and put it somewhere...
PLEASEEEE HELPPP IM BEING TIMEDDD WILL GIVE BRAINLIEST AND POINTS
Choose the polynomial written in standard form.
xy2 + 4x4y + 10x2
x4y2 + 4x3y + 10x
x4y2 + 4x3y5 + 10x2
x6y2 + 4x3y8 + 10x
Answer:
Can you please organize them so that the exponents are marked as x^2?
Step-by-step explanation:
To me, none of this is in standard form because the numbers are before the variables.
Will choose brainliest! How would you do this problem?
Answer:
[tex]c=8[/tex]
Step-by-step explanation:
When we plug in the solution [tex](x+2)[/tex], we will substitute [tex]x=-2[/tex], as [tex]-2+2=0[/tex].
To be divisible, a remainder of zero must be yielded.
Let's substitute [tex]x=-2[/tex] to see what we need to make [tex]c[/tex]:
[tex]p(-2)=4\cdot(-2)^3+c\cdot (-2)^2+(-2)+2,\\p(-2)=-32+4c[/tex]
Remember that we want a remainder of zero:
[tex]-32+4c=0,\\4c=32,\\c=\boxed{8}[/tex]
f(x) = 2x^2 – 3x - 9
g(x) = 4x^2 – 9
Find (f/g)(x)
Answer:
i dont get it sorry
Step-by-step explanation:
I need help help please help
middle left my guy lol..
Convert 8 1/6 into an improper fraction
Answer:
49/6
Step-by-step explanation:
8×6= 48
+ the numerator
The mixed fraction number in the form of an improper fraction will be 49/6.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The mixed fraction number is given below.
⇒ 8 ¹/₆
Convert the mixed fraction number into an improper fraction. Then we have
⇒ 8 ¹/₆
⇒ 8 + 1/6
⇒ (48 + 1) / 6
⇒ 49 / 6
The mixed fraction number in the form of an improper fraction will be 49/6.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
Lexie started her homework at 4:30 P.M. She finished at 5:05 P.M. How many seconds did it take her to finish her homework?
Answer:
2100 seconds
Step-by-step explanation:
4:30 P.M. → 5:05 P.M. there are 35 minutes in between.
1 minute = 60 seconds
35 minutes × 60 seconds = 2100 seconds
You roll a standard number cube. Find P (number greater than 5)
Answer:
1/6
Step-by-step explanation:
The numbers 24, 22, 34, 28, 29, 24, 25 29, a and b have a median of 27 and a mode of 29. Given that a
Answer: Median is 26,5 and modes are 24 and 29
Step-by-step explanation: In increasing order numbers are
22, 24 24, 25 , 28, 29 , 29 , 34. Because amount of number is even
median is (25 + 28) / 2 = 26,5 and modes are 24 and 29 because both
numbers exist twice
In a given triangle, side "a" is 7 inches long and side "b" is 24 inches long. The length of side "c" is
Answer:
25
Step-by-step explanation:
the formula for the hypotenuse of a triangle is
a^2+b^2=c^2
plug in what we know
7^2+24^2=c^2
49+576=c^2
625=c^2
c=25
hope this helps
Solve the equation 18 = 3 + 5x for x.
OA) 1
OB) 2
O C) 3
OD 4
Step-by-step explanation:
18 = 3 + 5x
15=5x
x=15/5
x=3
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {C) \:x\:=\:3}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]18 = 3 + 5x[/tex]
➺[tex] \: 5x = 18 - 3[/tex]
➺[tex] \: 5x = 15[/tex]
➺[tex] \: x = \frac{15}{5} [/tex]
➺[tex] \: x = 3[/tex]
[tex]\sf \bf {\boxed {\mathbb {To\:verify:}}}[/tex]
[tex]18 = 3 + 5x[/tex]
➺[tex] \: 18 = 3 + 5 \times 3[/tex]
➺[tex] \: 18 = 3 + 15[/tex]
➺[tex] \: 18 = 18[/tex]
➺[tex] \: L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
1. If segments MN, NO, and MO are tangent to circle P, find x.
70
x
•Р
2 m
M
N
-10 m
2 m
5 m
6 m
8 m
Answer:
Step-by-step explanation:
8m
The quality assurance engineer of a receiving-sets manufacturer inspects receiving-sets in lots of 50. He selects 4 of the 50 receiving-sets at random and inspects them thoroughly. Assuming that 5 of the 50 receiving-sets in the current lot are defective, find the probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.
Answer:
0.0430 = 4.30% probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.
Step-by-step explanation:
Sets are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Lots of 50 means that [tex]N = 50[/tex]
5 are defective, which means that [tex]k = 5[/tex]
4 are selected, which means that [tex]n = 4[/tex]
Find the probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.
This is [tex]P(X = 2)[/tex]. So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,50,4,5) = \frac{C_{5,2}*C_{45,2}}{C_{50,4}} = 0.0430[/tex]
0.0430 = 4.30% probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.
- Mona Allen wants to buy a bed that costs $695. The city sales tax rate is 7%. In a nearby city the sales tax rate is 4%. How much less would the bed cost if Mona bought it in the nearby city?
Answer:
$20.85 less.
Step-by-step explanation:
City sales:
7% tax = 48.65
total bed cost = $743.65
Nearby City:
4% tax = 27.8
total bed cost = $722.8
city sale - nearby city
743.65 - 722.8
=20.85
How many lines intersect at point O?
A.2
B.1
C.4
D.3
Answer:
C. 4 because line o serve as the vertex for each angle there.