A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers the color green. If 14 buyers are randomly selected, what is the probability that exactly 12 buyers would prefer green

Answers

Answer 1
Answer:

Answer:

The probability that exactly 12 buyers would prefer green

=0.00555

Step-by-step explanation:

We are given that

p=50%=50/100=0.50

n=14

We have to find the probability that exactly 12 buyers would prefer green.

q=1-p

q=1-0.50=0.50

Using binomial distribution formula

P(X=x)=nC_r p^r q^(n-r)

P(x=12)=14C_(12)(0.50)^(12)(0.50)^(14-12)

P(x=12)=14C_(12)(0.50)^(12)(0.50)^2

P(x=12)=14C_(12)(0.50)^(14)

P(x=12)=(14!)/(12!2!)(0.50)^(14)

P(x=12)=(14* 13* 12!)/(12!2* 1)(0.50)^(14)

P(x=12)=91\cdot (0.50)^(14)

P(x=12)=0.00555

Hence, the probability that exactly 12 buyers would prefer green

=0.00555


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Answers

For this case we have the following equation:
 y = 4 (x-2) ^ 2-1
 Rewriting we have:
 y = 4 (x ^ 2-4x + 4) ^ 2-1
 Multiplying the common factor 2 we have:
 y = 4x ^ 2-16x + 16-1
 Adding the constant term we have:
 y = 4x ^ 2-16x + 15
 Answer:
 
y = 4x ^ 2-16x + 15
 
option D
the answer is D y=4x^2-16x+15

According to a poll, 76% of California adults (385 out of 506 surveyed) feel that education is one of the top issues facing California. We wish to construct a 90% confidence interval for the true proportion of California adults who feel that education is one of the top issues facing California. Find the error bound. (Round your answer to three decimal places.)

Answers

Answer:

The error bound is 3.125%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence interval 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{(\pi(1-\pi))/(n)}

In which

z is the zscore that has a pvalue of 1 - (\alpha)/(2).

For this problem, we have that:

A sample of 506 California adults.. This means that n = 506.

76% of California adults (385 out of 506 surveyed) feel that education is one of the top issues facing California. This means that \pi = 0.76

We wish to construct a 90% confidence interval

So \alpha = 0.10, z is the value of Z that has a pvalue of 1 - (0.10)/(2) = 0.95, so z = 1.645.

The lower limit of this interval is:

\pi - z\sqrt{(\pi(1-\pi))/(n)} = 0.76 - 1.645\sqrt{(0.76*0.24)/(506)} = 0.7288

The upper limit of this interval is:

\pi + z\sqrt{(\pi(1-\pi))/(n)} = 0.76 + 1.645\sqrt{(0.76*0.24)/(506)} = 0.7913

The error bound of the confidence interval is the division by 2 of the subtraction of the upper limit by the lower limit. So:

EBM = (0.7913 - 0.7288)/(2) = 0.03125

The error bound is 3.125%.

The smaller of two consecutive numbers is x + 3. Find the sum of the two numbers.

Answers

Answer:

x+3. is the first num

x +4 is the second num

the sum is 2x +7

Answer:

2x + 7

Difference is 1

Step-by-step explanation:

Consecutive numbers are numbers that increase with a steady difference.

For example; 1, 2, 3 all increase with a difference of 1 (2 = 1 + 1; 3 = 2 + 1) and so on.

If the smaller of two consecutive numbers is x + 3, that means the other number which should be bigger is x + 4

Therefore the sum of both numbers is (x + 3) + (x + 4) = 2x + 7.

Their difference is (x + 4) - (x + 3) = 1

And subtracting their sum from x + 8 gives (x + 8) - (2x + 7) = x + 8 - 2x - 7 = -x + 1.

a discount voucher offering 15% off is used to pay a bill. after using the voucher the bill is reduced to 36.72. how much was the bill before applying the voucher discount

Answers

We can use the is/of=p/100 method for this problem. Since it's 15% off, this would mean that the bill is 85% of what it was initially. Plug the values into the is/of=p/100 formula.

36.72/x = 85/100

Solve  for x.

x=36.72/0.85

x=43.2

So, the bill was $43.20 before applying the voucher discount of 15% off.


The answer is 244.80

You can calculate this by taking 36.72 and dividing it by 0.15 (15%). You would do this because it is the opposite of multiplying an original number by 0.15 (15%) to get 36.72.


Hope It helps!

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In a survey of 269 college students, it is found that69 like brussels sprouts,
90 like broccoli,
59 like cauliflower,
28 like both Brussels sprouts and broccoli,
20 like both Brussels sprouts and cauliflower,
24 like both broccoli and cauliflower, and
10 of the students like all three vegetables.

a) How many of the 269 college students do not like any of these three vegetables?

b) How many like broccoli only?

c) How many like broccoli AND cauliflower but not Brussels sprouts?

d) How many like neither Brussels sprouts nor cauliflower?

Answers

Answer: a) 83, b) 28, c) 14, d) 28.

Step-by-step explanation:

Since we have given that

n(B) = 69

n(Br)=90

n(C)=59

n(B∩Br)=28

n(B∩C)=20

n(Br∩C)=24

n(B∩Br∩C)=10

a) How many of the 269 college students do not like any of these three vegetables?

n(B∪Br∪C)=n(B)+n(Br)+n(C)-n(B∩Br)-n(B∩C)-n(Br∩C)+n(B∩Br∩C)

n(B∪Br∪C)=69+90+59-28-20-24+10=156

So, n(B∪Br∪C)'=269-n(B∪Br∪C)=269-156=83

b) How many like broccoli only?

n(only Br)=n(Br) -(n(B∩Br)+n(Br∩C)+n(B∩Br∩C))

n(only Br)=90-(28+24+10)=28

c) How many like broccoli AND cauliflower but not Brussels sprouts?

n(Br∩C-B)=n(Br∩C)-n(B∩Br∩C)

n(Br∩C-B)=24-10=14

d) How many like neither Brussels sprouts nor cauliflower?

n(B'∪C')=n(only Br)= 28

Hence, a) 83, b) 28, c) 14, d) 28.

Jimmy purchased a government bond which has maturity value of $2500 after 9 months at 11 % simple interest. How much should he pay for this bond?

Answers

Answer: he should pay $23095 for this bond.

Step-by-step explanation:

We would apply the formula for determining simple interest which is expressed as

I = PRT/100

Where

I represents interest paid on the bond purchased.

P represents the principal or amount of bond purchased.

R represents interest rate

T represents the duration of the bond in years.

From the given information,

R = 11%

T = 9 months = 9/12 = 0.75

I = 25000 - P

Therefore

25000 - P = (P × 11 × 0.75)/100

25000 - P = 8.25P/100 = 0.0825P

P + 0.0825P = 25000

1.0825P = 25000

P = 25000/1.0825

P = $23095

Answer:$2706.25

Step-by-step explanation:

Principal(t)=$2500

Time(t)=9months=9/12=0.75year

Rate(r)=11%

Simple interest(si)=?

Si=(pxrxt)/100

Si=(2500x11x0.75)/100

Si=20625/100

Si=$206.25

Total amount=p + si

Total amount=2500+206.25

Total amount=$2706.25

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