Answer:
a. P(X = 3) = 0.145736
b. P(5≤X≤9) = 0.5462
c. P(5<X<10) = 0.3332
d. P(X≥6) = 0.3393
e. P(X<5) = 0.4477
f. Mean = 4.8, Variance = 3.264
Step-by-step explanation:
Given - The same survey database cited in exercise 4.3.1 (A-5) shows
that 32 percent of U.S. adults indicated that they have been
tested for HIV at some point in their life. Consider a simple
random sample of 15 adults selected at a time. Let X be the
number of adults who have been tested for HIV in the sample.
To find - For the following, find the numerical answer and describe
the answer in words:
a. Three
b. Between five and nine, inclusive
c. More than five, but less than 10
d. Six or more
e. Less than five
f. Find the mean and the variance of the number of people
tested for HIV in samples of size 15.
Proof -
Given that , n = 15, p = 32% = 0.32
Now,
a.
P(X = 3) = binomial distribution (3, 15, 0.32, 0)
= [tex]\left(\begin{array}{ccc}15\\3\end{array}\right)(0.32)^{3}(1-0.32)^{15 - 3}[/tex]
= 455(0.032768)(0.009774)
= 0.145736
⇒P(X = 3) = 0.145736
b.
P(5≤X≤9) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
= [tex]\left(\begin{array}{ccc}15\\5\end{array}\right)(0.32)^{5}(1-0.32)^{15 - 5}[/tex]+ [tex]\left(\begin{array}{ccc}15\\6\end{array}\right)(0.32)^{6}(1-0.32)^{15 - 6}[/tex] + [tex]\left(\begin{array}{ccc}15\\7\end{array}\right)(0.32)^{7}(1-0.32)^{15 - 7}[/tex] + [tex]\left(\begin{array}{ccc}15\\8\end{array}\right)(0.32)^{8}(1-0.32)^{15 - 8}[/tex]+ [tex]\left(\begin{array}{ccc}15\\9\end{array}\right)(0.32)^{9}(1-0.32)^{15 - 9}[/tex]
= 0.213 + 0.1671 + 0.1011 + 0.0476 + 0.0174
= 0.5462
⇒P(5≤X≤9) = 0.5462
c.
P(5<X<10) = + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
= [tex]\left(\begin{array}{ccc}15\\6\end{array}\right)(0.32)^{6}(1-0.32)^{15 - 6}[/tex] + [tex]\left(\begin{array}{ccc}15\\7\end{array}\right)(0.32)^{7}(1-0.32)^{15 - 7}[/tex] + [tex]\left(\begin{array}{ccc}15\\8\end{array}\right)(0.32)^{8}(1-0.32)^{15 - 8}[/tex]+ [tex]\left(\begin{array}{ccc}15\\9\end{array}\right)(0.32)^{9}(1-0.32)^{15 - 9}[/tex]
= 0.1671 + 0.1011 + 0.0476 + 0.0174
= 0.3332
⇒P(5<X<10) = 0.3332
d.
P(X≥6) = 1 - P(X < 6)
= 1 - P(X ≤ 5)
= 1 - binomial(5, 15, 0.32, 1)
= 1 - 0.6607
= 0.3393
⇒P(X≥6) = 0.3393
e.
P(X<5) = P(X≤4)
= binomial (4, 15, 0.32, 1)
= 0.4477
⇒P(X<5) = 0.4477
f.
Mean = np
= 15(0.32)
= 4.8
⇒Mean = 4.8
Variance = np(1-p)
= 15(0.32)(1 - 0.32)
= 4.8(0.68)
= 3.264
⇒Variance = 3.264
Which expression is equivalent to 1/4(2 – 5x + 6)?
Answer: the answer is CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C
Which digit in the following number is the one that determines its precision? 2801.3
The answers 3
Answer:
3
Step-by-step explanation:
. Robbie decides to make 12 batches of chicken noodle soup. How much ground black pepper should he use? ( THERE ARE 1/8 TEASPOON OF GROUNDPM PEPPER IN ONE BATCH) pls put in fraction form
the answer for your question is 1 1/2
An elliptical table is being cut from a rectangular piece of wood that is 12 feet by 10 feet. Legs of the table will be
attached at the foci. Which equation models the largest ellipse that can be cut from the rectangle and describes
where the legs will be attached?
Answer:
B on edge
Step-by-step explanation:
just got it wrong
What is the measure of angle R?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
mZR
=
Answer:
m<R = 22.62°
Step-by-step explanation:
Reference angle = R
Opposite = 5 cm
Hypotenuse = 13 cm
Apply the trigonometric function SOH:
Sin R = Opp/Hyp
[tex] Sin (R) = \frac{5}{13} [/tex]
[tex] R = sin^{-1}(\frac{5}{13}) [/tex]
R = 22.6198649°
m<R = 22.62° (nearest hundredth)
Simplify the expression.
4.6r + 2.8r
plz help fast plz plz plz
Answer: -6
Step-by-step explanation:
Consider circle E.
A
B
26
D
E
F
What is the mBC ?
mBC
Please help
Step-by-step explanation:
< AEB + < BEC = 180° {BEING LINEAR PAIR }
26° + < BEC = 180°
< BEC = 180° - 26°
< BEC = 154°
ARC BC = < BEC ( relation between arc and central angle)
Arc BC = 154°
Hope it will help :)
what is the volume of a hemisphere with a diameter of 41.6m, rounded to the nearest 10th of a cubic meter
Explanation is in the file
tinyurl.com/wtjfavyw
find the area of iscolces triangle 13cm
b=2A
hb
For an isosceles triangle, the area can be easily calculated if the height (i.e. the altitude) and the base are known. Multiplying the height with the base and dividing it by 2, results in the area of the isosceles triangle.
The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 31 hours and the median is 27.2 hours. Twenty-four of the families in the sample turned on the television for 1616 hours or less for the week. The 7th percentile of the data is 16 hours. Based on the given information, determine if the following statement is true or false.
The 56th percentile is greater than or equal to 26 hours.
a. True
b. False
Answer:
False
Step-by-step explanation:
Solve these and show your work pls!
Answer :the 1st and 3rd are true
Step-by-step explanation:
you do the math how their set up so just right those and you can get your answer that way. (if your adding a positive and negative your basically subtracting so just write in the order their in; if you subtracting a negative from a positive it equals a positive; if your subtracting a negative from a negative or the answer is positive; if your subtracting a positive from a negative its negative) i hope this helps if u have any more questions just message me and i will be happy to help you anytime!!! <3
5=10+n/6
5(6)=10+n(6)
30=10+n
-10 -10
Answer: sooooo....... the answer is n=20
Step-by-step explanation: did you really needed the answer for this?
Answer:
n = -30
Step-by-step explanation:
5 = 10 + n/6
-5 = n/6
n = -30
Which graph shows an increasing linear function? p.s dont mind the tabs lol!!!
Cot^2x+1 please simplify
The number of cars in 25 families is shown in the table. Calculate the mean number of cars in a family.
No of cars Frequency
1 5
2 10
3 7
4 2
5 1
Answer:
Mean = 11.8
Step-by-step explanation:
Given the following data;
Total number of cars (n) = 5
Number of cars (x) = 1, 2, 3, 4, 5
Frequency (F) = 5, 10, 7, 2, 1
F(x) = (1*5) + (2*10) + (3*7) + (4*2) + (5*1)
F(x) = 5 + 20 + 21 + 8 + 5
F(x) = 59
To find the mean;
Mean = F(x)/n
Mean = 59/5
Mean = 11.8
3x2^+2(x+4x) when x=2
Answer:
32
Step-by-step explanation:
Given the algebraic expression;
[tex] 3x^{2} + 2(x + 4x) = 0 [/tex]
When x = 2
It simply means that we would substitute the value of x into the equation.
[tex] 3*2^{2} + 2(2 + 4*2) [/tex]
[tex] 3*4 + 2(2 + 8) [/tex]
[tex] 12 + 2(10) [/tex]
[tex] 12 + 20 [/tex]
[tex] 12 + 20 = 32 [/tex]
code is formed using four of these letters: A, B, I. K, N, O, and T. (Note that the order of the letters in the code matters; for example, ABIK
different code from BAIK.
The size of the sample space is
. The probability that the first three letters of the four-letter code are vowels is
Answer:
The size of the sample is 840.
The probability that the first three letters of the four-letter code are vowels is=\frac{1}{35}=
35
1
Step-by-step explanation:
Th total number of letters given to form code of 4 letters = 7
Since, the order of the letters in the code matters, which means there is no repetition.
The total number of ways to form the code size =7*6*5*4=8407∗6∗5∗4=840
Therefore, The size of the sample is 840.
Since, there are 3 vowels and rest of 4 letters are consonant.
The number of ways to form code such that the first three letters of the four-letter code are vowels =3\times2\times1\times4=243×2×1×4=24
The probability that the first three letters of the four-letter code are vowels is
=\frac{24}{840}=\frac{1}{35}
840
24
=
35
1
Each side of a square piece of glass is 8 centimeters long. What is the piece of glass's area?
Answer:
area=l²
l=8
area=8²
=8×8
=64
The piece of glass's area is is 64 square cm.
What is the length of the square?Diagonals of a Square A square has two diagonals, they are equal in length and intersect in the middle.
The length of square is given by;
[tex]\rm Length =a^2[/tex]
Each side of a square piece of glass is 8 centimeters long.
The piece of glass's area is;
[tex]\rm Glass \ area=a^2\\\\ Glass \ area=8^2\\\\ Glass \ area=64[/tex]
Hence, the piece of glass's area is is 64 square cm.
Learn more about square length here;
https://brainly.com/question/11472698
#SPJ2
if arc lm = 20 ft, find the radius of N
Answer:
120 ft
Step-by-step explanation:
60/360 or 1/6 of circle = 20 ft
full circle = 20 x 6 = 120 ft
diameter = 120/3.14 = 38.22 ft
radius = 38.22/2 = 19.11 ft
Answer:
Step-by-step explanation:
60° = ⅙ of 360°, so length of arc LM = ⅙ of 2πr.
20 = 2πr/6
r = 60/π ft
A video game store is selling video games 3 for $37.50. How much would they earn if they sold 2?
Answer:
25
Step-by-step explanation:
ok so you need to find out how much each game is sold for
First 37.50 divided by 3 and that will equal 12.5
second, you need to find out how much 2 games cost so you eithermultiply
12.5 by 2 or add 12.5 two times and you will get 25
hope this helped;)
Solve for X in the figure below, knowing line L is parallel to line M. Thank You!
Answer:
3x+5= 65°( alternate interior angles)
3x=60
x=60/3=20°
Step-by-step explanation:
Answer:
x = 18.67
Step-by-step explanation:
3x + 5 = 61
-5 -5
3x = 56
divide by 3
x = 18.67
Which expression is equivalent to f(x)=6x^2-13x+5
Answer:
(3x - 5)(2x - 1)
Step-by-step explanation:
6x² - 13x + 5
6x² - (10 + 3)x + 5
6x² - 10x - 3x + 5
2x(3x - 5) - (3x - 5)
(3x - 5)(2x - 1)
Which means, 6x² - 13x + 5 is equivalent to (3x - 5)(2x - 1) or vice versa
help pleaseee i need this
If a regression analysis shows an R factor of 0.15, it is safe to assume a perfect positive relationship between cost and volume. a strong negative relationship between cost and volume. a strong positive relationship between cost and volume. a very weak relationship between cost and volume.
Answer:
a very weak relationship between cost and volume
Step-by-step explanation:
The R factor is used to access the strength of the relationship between a dependent and independent variable. The R factor ranges between - 1 and 1. With negative values depicting a negative linear relationship and positive values meaning a positive relationship. The closer the R factor is to - 1 or + 1, the greater the strength, a value of 0 means, no correlation exists.
Hence, a R factor of 0.15 depicts a positive but very weak relationship between cost and volume as the R value is close to 0.
PLS HELP WILL GET BRAINIEST A'B'C'is a translation of ABC. What is the length of A'C'?
Answer:
6 units
Step-by-step explanation:
There is only a translation being shown, meaning that the shape is only moving. It is not getting larger or smaller.
Answer:
your answer will be option C.6
because the length does not change on translation
Step-by-step explanation:
have a nice day
3. Temperature
(THIS IS NOT A MULTIPLE CHOICE)
Answer:
a) clusters: none, gaps: 99, and 100, peaks: 101, outliers: none.
b) center of distribution:
median: 101, mean: 99.9090.
(a)
The outliers are the values that are far from the middle.
In this case, the outliers are 97, 98, 98, 98.
A cluster occurs when the data occurs within a small interval.
In this case, there's a cluster between 100 and 102.
According to the dot plot, there's a gap from 98 to 101.
At last, the peak is at 101, which is the value with the highest frequency.
(b)
The given data set doesn't form a normal distribution because there's no data in the middle of the data set, instead, there's a gap. Additionally, the spread or range of the data set is 5, where the majority of the data is not in the middle which mean the dispersion of the data is important.
Find the area of the triangle below.
6
18
A =
units squared
Answer:
hhhdddhhsuuwuwuww?w?w?
Find the difference f(x) - g(x) for functions f(x) = 6x^{2} + 2x -14 and g(x) = -x^{2} + 10x - 4
5x^{2} + 8x - 10
5x^{2} + 12x - 18
-7x^{2} + 12x - 18
7x^{2} - 8x - 10
Answer:
Your answer is the 4th one , 7xpower2 - 8 x - 10
Raul borrows $600 at an interest rate of 8% per year for 4 years. How much simple interest will he have to pay?
__________________________________
A = P × i × n = $600 × 8% × 4 Years= $192= $600 + $192= $2,619Raul Will Have To Pay $2,619__________________________________