Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.05?
If it was later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Why?
a. If the confidence level is increased, then the sample size would need to increase because a higher level of confidence increases the margin of error.
b. If the confidence level is increased, then the sample size would need to decrease because increasing the sample size would create an even larger interval.
c. If the confidence level is increased, then the sample size would need to decrease because we would like the proportion of people who buckle up to be around 50%.
d. If the confidence level is increased, then the sample size would not be affected.
Answer:
The value is [tex]n = 384 [/tex]
The correct option is a
Step-by-step explanation:
From the question we are told that
The margin of error is E = 0.05
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally since the sample proportion is not given we will assume it to be
[tex]\^ p = 0.5[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{ 1.96 }{0.05} ]^2 *0.5 (1 - 0.5) [/tex]
=> [tex]n = 384 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
Generally if the level of confidence increases, the critical value of [tex]\frac{\alpha }{2}[/tex] increase and from the equation for margin of error we see the the critical value varies directly with the margin of error , hence the margin of error will increase also
So If the confidence level is increased, then the sample size would need to increase because a higher level of confidence increases the margin of error.
one student can paint a wall in 10 minutes another student can paint the same wall in 15 minutes working together how long will it take for them to paint the wall?
Answer:
6 min
Step-by-step explanation:
given that the rate for the first student is 10 min per wall
we can express this in wall per minute by taking the reciprocal
hence student 1's unit rate = 1/10 wall per min
similarly, we can express student 2's unit rate as 1/15 wall per min.
if we add up the two, we will get the amount of wall painted by two people working together per min
amount of wall painted per min by 2 people
= wall per min of person 1 + wall per min of person 2
= 1/10 + 1/15
= 3/30 + 2/30
= 5/30
= 1/6 wall per min.
to convert this to minutes per wall, we take the reciprocal:
number of minutes that both people will take to paint the wall
= 1 / (1/6)
= 6 min per wall (answer)
16x^2+25 factor completely
Answer:
You can't factor further
Hope this helps!
If an AaBbccDd individual is crossed to a AaBbCcDD individual, what is the probability that the first offspring will be of AabbccDd genotype?
Answer:
The probability that the first offspring will be of AabbccDd genotype is 0.03125.
Step-by-step explanation:
The parents genotype are: AaBbccDd and AaBbCcDD.
Aa and AaA a
A AA Aa
a Aa aa
P (Aa) = 2/4 = 1/2
Bb and BbB b
B BB Bb
b Bb bb
P (bb) = 1/4
Cc and ccc c
C Cc Cc
c cc cc
P (cc) = 2/4 = 1/2
Dd and DDD d
D DD Dd
D DD Dd
P (Dd) = 2/4 = 1/2
Then the probability that the first offspring will be of AabbccDd genotype is:
P (AabbccDd) = (1/2) × (1/4) × (1/2) × (1/2) = 1/32
Thus, the probability that the first offspring will be of AabbccDd genotype is 0.03125.
Lisa spends the same amount of time doing homework each day on Monday she spents of half of her time studying for a history test. on Tuesday, she spent 3/5 of her time studying for the same test in
the two days she spenta bal of 3 hours and 29 minutes studying for the test How much time does
she spend ting homework each day
Work out (7×10^5) ÷ (2×10^2)
Give
your answer in standard form.
Answer:
3.5 X 10^3
Step-by-step explanation:
The function h(x) = 2x – 8+ 1 is a transformation of the parent function f(x) = x. Select all the statements that describe a key feature of function h.
Answer:
1
4
5
Step-by-step explanation:
An item that cost $220 has been marked up by 15% since last year. However, a person can buy the item for a 25%
employee discount. How much will the employee pay?
Answer:189.75
Step-by-step explanation: 220 * 0.15 = 33
220 + 33 = 253
253 * 0.25 = 63.25
253 - 63.25 = 189.75
David has available 40 yards of fencing and wishes to enclose a rectangular area.
Answer:
5 units will be your width and 15 will be your length so it would look like side#1=5 side #2=15 side number3 is 5 and side number 4 is 15 assuming that side 1 and 3 are parallel.
Step-by-step explanation:
yes
Free brainliest timmmmmmme :)
What is 2+2?
A. 69
B. 420
C:666
D:21
PLEASE HELP WORTH 4 POINTS
Answer:
2+2=4
Step-by-step explanation:
lol tell me the subject and ill research and give u n answer
An electric company charges each of its customers a monthly fee of $19 to maintain the account and nine cents per kilowatt hour what is an equation that relates the monthly cost c in dollars of power consumed P in kilowatt hours 
Answer:
c = 19 + 0.09P
Step-by-step explanation:
The total cost is the $19 monthly fee plus the amount per hour.
c = 19 + 0.09P
Rewrite the equation below so that it does not have fractions.
4+3/4x=5/6
do not write any decimal
Answer:
x=-18/76
Step-by-step explanation:
4×4x/4x+3/4x=5/6
or,96x+18=20x
or,76x=-18
:x=-18/76 ans...
3. $590 is deposited into a
savings account that earns
4.3 % simple interest for 3
years.
Answer:
615.37
Step-by-step explanation:
590 x 1.043
Hope I helped!
Emile paid $3.96 for 4 songs.
What is the unit rate and what does it mean?
Enter your answers in the boxes.
Answer:
$0.99
Unit rate is cost for 1 individual (song)
Step-by-step explanation:
$3.96/4
0.99
99 cents
Can you solve this?: 5+2x=12+x
Answer:
5+2x=12+x
put all numbers and Xs on one side each
-x=7
so x=-7
What would be the answee
What do you add to 43/6 to make 7
Answer:
1/6 that's the answer
Step-by-step explanation:
so you do 43/6-7=43/6-42/6=1/6
Answer:
Actually the answer is -⅙
Step-by-step explanation:
43/6 written differently is 7 ⅙, because the fraction 42/6 is the same as 7 (42÷6=7). But since your number is 43/6 you get
7 1/6.
your original number is larger than 7 but the question was what number you have to "add" to get to 7. so they number has to be a negative number.
like this:
43/6 + (-1/6) = 42/6. which you rewrite now as
43/6 - 1/6 = 42/6. and I explained that 42/6 is the same as 7.
What is 20 divided by 740 with remainder
Answer:
37 R0
Step-by-step explanation:
740/20=37, so there is no remainder.
I hope this helps you! Have a great day c:
Dividing 20 by 740 gives us remainder 20 and quotient 0.
To find the result of 20 divided by 740 with a remainder,
Perform the division and take note of the quotient and remainder.
20 ÷ 740 = 0 with a remainder of 20.
Division is a mathematical operation that involves splitting a number (the dividend) into equal parts,
with a divisor indicating how many parts we want to split it into.
The quotient is the number of equal parts, and the remainder is what's left after have split the dividend into as many equal parts as possible.
20 divided by 740, we are trying to find out how many times 740 can fit into 20.
Since 740 is much larger than 20, it cannot fit even once.
So, the quotient is 0, indicating that 0 whole units of 740 can fit into 20.
However, there is a remainder of 20.
The remainder represents the portion of 20 that cannot be evenly divided by 740.
It is what remains after we have divided the dividend by the divisor as many times as possible.
Therefore, 20 divided by 740 is 0 with a remainder of 20.
learn more about remainder here
brainly.com/question/29019179
#SPJ2
what is the correct standard form for 30+2+0.1+0.005
Answer:
32.105
Step-by-step explanation:
30
2
+ 0.1
0.005
32.105 so answer is 32.105
$6,000 is invested in an account at interest rate r, compounded continuously. Find the time (in years) required for the amount to double when r= 9.5% and when r=2.5%.
Answer: When r= 9.5% , time = 7.3 years
When r= 2.5% , time = 27.7 years
Step-by-step explanation:
Exponential equation for compounded continuously:
[tex]A=Pe^{rx}[/tex] , where P= Principal value invested , r= rate of interest, x= time
Given : P= $6,000
A = 2P= 2 ($6,000) = $12,000 (i)
When r= 9.5%= 0.095
[tex]A= 6000e^{0.095x}[/tex] (ii)
From (i) and (ii)
[tex]6000e^{0.095x}=12000\\\\\Rightarrow\ e^{0.095x}=2\\\\\Rightarrow\ \ln e^{0.095x} =\ln 2\\\\\Rightarrow\ 0.095x=0.693147\\\\\Rightarrow\ x=\dfrac{0.693147}{0.095}=7.296284210\approx7.3 \text{ years}[/tex]
For r= 2.5% = 0.025
[tex]6000e^{0.025x}=12000\\\\\Rightarrow\ e^{0.025}=2\\\\\Rightarrow\ \ln e^{0.025x} =\ln 2\\\\\Rightarrow\ 0.025x=0.693147\\\\\Rightarrow\ x=\dfrac{0.693147}{0.025}=27.72588\approx27.7 \text{ years}[/tex]
I WILL REWARD BRAINLIEST OKAY IM BEGGING YOU HELP ME
IN THAT PHOTO WHAT ARE THE X AND Y INTERCEPTS!?! WAIT DON'T LOOK AT THE PHOTO YET!!
PLEASE LOOK AT THIS EXAMPLE:
X intercept: ( ), ( )
Y intercept: ( ), ( )
NOW LOOK. AT THE PHOTO PLEASE!!
Answer:
X-intercept: -10
Y-intercept: -45
(-10),(-45)
Step-by-step explanation:
Hop this helped, Have a Wonderful Day!!
What is the DOMAIN of this graph?
Answer:
Is yellow
Step-by-step explanation:
an open circle for "less than" or "greater than", and a closed circle for "less than or equal to"
One-eighth of a number is -4,200.
What is the number?
-42,800
-37,800
-33,600
-42,000
Answer:
33,600
Step-by-step explanation:
take -4200 and multiply it by 8. You'd do this since the equation to get -4200 is
x(1/8) = -4200
multiply both sides by 8 to get rid of the fraction and you get x=33,600
PLZZZZZZZZZZZZZZZZZZZZZZ HELP!
-3x+4=-2 show your work!!!
Answer:
x=2
Step-by-step explanation:
The function t= 21.55 cos (pi/6(m-7)) + 43.75 models the average high temperature in degrees Fahrenheit each month
Answer:
B - 8
Step-by-step explanation:
Answer:
answer is letter b 8
Step-by-step explanation:
HELP PLEASE the second one is a match question
Answer:
1)Coefficient
2)Dividend
3) Quotient
Step-by-step explanation:
i need help pls i cant understand my math hw
Answer:
Ok
Step-by-step explanation:
So what are we magically supposed to know what the equation is
Answer:
uh
Step-by-step explanation:
for us to help please write the question you are stuck on
Allan wanted to become a machine salesperson. He was offered a job that paid him $40,000 a year plus a commission of $300 for every machine he sells. If Allan made &50,800 last year, how many machine did he sell?
Answer:
36
Step-by-step explanation:
50800-30000=10800/300=36
:)
An integer is 15 more than 2 times another. If the product of the two integers is -27, then find the integers
Answer:
The required integers are x=3 and y= -9
Step-by-step explanation:
Let one the integers be x and y
An integer is 15 more than 2 times another: x=15+2y
product of the two integers is -27: x*y=27
[tex]x=15+2y ---eq(1)\\x*y=-27----eq(2)[/tex]
Solving both equations to find values of x and y
Putting value of x from equation 1 in equation 2
[tex](15+2y)*y=-27\\15y+2y^2=-27\\Rearranging:\\2y^2+15y-27=0[/tex]
This can be solved using quadratic formula:
[tex]$y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
Putting values and finding factors
[tex]$y=\frac{-(15)\pm\sqrt{(15)^2-4(2)(-27)}}{2(2)}$\\$y=\frac{-(15)\pm\sqrt{225+216}}{4}$\\$y=\frac{-(15)\pm\sqrt{441}}{4}$\\$y=\frac{-(15)\pm21}{4}$\\$y=\frac{-(15)+21}{4} \ or \ y=\frac{-(15)-21}{4}$\\$y=\frac{6}{4} \ or \ y=\frac{-36}{4}$\\$y=\frac{3}{2} \ or \ y=-9$[/tex]
Since y is integer so, we consider only y= -9
The value of x will be:
[tex]x*y=-27\\x*(-9)=-27\\x=\frac{-27}{-9} \\x=3[/tex]
So, the value of x is x=3
The required integers are x=3 and y= -9
<3 and <4 are vertical. m<3=5x+22 and m<4=7x+2. Find the measure of each angl.
Answer:
72°
Step-by-step explanation:
Vertical angles are congruent.
m∠3 = m∠4
7x + 2 = 5x + 22
2x = 20
x = 10
m∠3 = m∠4 = 72°