Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 10. Use the empirical rule to determine the following
Answers
Solution
We are given
[tex]\begin{gathered} Mean(\mu)=100 \\ S\tan dardDeviation(\sigma)=10 \end{gathered}[/tex]Note: Z score formula
[tex]Z=\frac{\bar{X}-\mu}{\sigma}[/tex](a). What percentage of people has an IQ score between 90 and 110?
[tex]\begin{gathered} p(90Therefore, the answer is[tex]p(90(b) What percentage of people has an IQ score less than 80 or greater than 120?Thus, we have
[tex]\begin{gathered} p(X<80)+p(X>120) \\ \text{For } \\ p(X<80)=p(Z<\frac{80-100}{10}) \\ p(X<80)=p(Z<-2) \\ p(X<80)=0.02275 \\ \text{Now for} \\ p(X>120)=p(Z>\frac{120-100}{10}) \\ p(X>120)=p(Z>2)=1-p(Z<2)=1-0.97725=0.02275 \\ \text{Therefore,} \\ p(X<80)+p(X>120)=0.02275+0.02275 \\ p(X<80)+p(X>120)=0.0455 \\ \text{Converting to percentage} \\ p(X<80)+p(X>120)=4.55\% \end{gathered}[/tex]Therefore, the answer is
[tex]p(X<80)+p(X>120)=4.55\%[/tex](C). What percentage of people has an IQ score greater than 120?
We have
[tex]\begin{gathered} p(X>120)=p(Z>\frac{120-100}{10}) \\ p(X>120)=p(Z>2)=1-p(Z<2)=1-0.97725=0.02275 \\ \text{Converting to percentage} \\ p(X>120)=2.275\% \end{gathered}[/tex]Therefore, the answer is
[tex]p(X>120)=2.275\%[/tex]Related Questions
In a survey of 29 instructors, it was found that 22 liked white boards, 11 liked blackboards, and 7 liked both. How many instructors did not like white boards?
Answers
We need to find the number of instructors that did not like whiteboards.
In order to do so, notice that from the 11 instructors who liked blackboards, 7 also liked whiteboards.
Thus, among the instructors who liked at least one of the two types of boards, the number of them who didn't like whiteboards is:
[tex]11-7=4[/tex]Also, there were some instructors among the whole group of 29 that didn't like any of the two boards. Thus, those ones didn't like whiteboards.
The following image illustrates this problem:
So, we need to find x and add it to the other 4 instructors that didn't like whiteboards.
We have:
[tex]\begin{gathered} 15+7+4+x=29 \\ \\ 26+x=29 \\ \\ x=29-26 \\ \\ x=3 \end{gathered}[/tex]Thus, another 3 instructors didn't like whiteboards.
Therefore, the total number of instructors who didn't like whiteboards is
[tex]4+3=7[/tex]Notice that we can find the same result in a faster way: since 22 instructors liked whiteboards from a total of 29 instructors, it means that 29 - 22 = 7 didn't like whiteboards.
Therefore, the answer is 7.
At the produce store you can buy 2 bags of bananas for $13.90. How muchwould it cost if you were to buy 7 bags?
Answers
ANSWER:
$ 48.65
STEP-BY-STEP EXPLANATION:
We can calculate the value of 7 bags with the help of the following proportion:
[tex]\frac{13.9}{2}=\frac{x}{7}[/tex]We solve for x, which would be the cost of the 7 bags, like this:
[tex]\begin{gathered} 13.9\cdot7=2\cdot x \\ x=\frac{97.3}{2} \\ x=48.65 \end{gathered}[/tex]The cost of 7 bags is $ 48.65
Simplify the ratio 15 to 21 is?
Answers
Given the ratio;
[tex]15\colon21[/tex]To simplify the above ratio, we would change the ratio to a fraction then divide the numerator and the denominator by the same value, and till we get to the lowest possible term.
This gives,
[tex]\begin{gathered} \frac{15}{21}\mleft\lbrace\text{Divide numerator and denominator by 3}\mright\rbrace \\ =\frac{5}{7} \\ \therefore5\colon7 \end{gathered}[/tex]Therefore, the answer is
Answer: 5:7
14.9x+1/3 (-12-27x)-33.2 , x=-3simplify the expression using the properties of operations.
Answers
14.9x+1/3 (-12-27x)-33.2
Using PEDMAS;
First, let's open the parenthesis
14.9x - 4 - 9x - 33.2
Rearrange
14.9x - 9x -4 -33.2
5.9x - 37.2
But from the question x= -3
Substitute x=-3 in the above;
5.9(-3) - 37.2
-17.7 - 37.2
-54.9
Using the formula for area of a rectangle, A = lw, solvefor the length, l.
Answers
ANSWER
[tex]l=\frac{A}{w}[/tex]EXPLANATION
We want to solve for the length, l, in the formula for the area of a rectangle:
[tex]A=lw[/tex]We simply want to make the length the subject of the formula. To do this, divide both sides of the formula by w:
[tex]\begin{gathered} \frac{A}{w}=\frac{lw}{w} \\ \Rightarrow l=\frac{A}{w} \end{gathered}[/tex]That is the answer.
This probability distribution shows thetypical distribution of the number of shoes
Answers
First, add the frequencies in order to obtain the total number of surveyed people,
[tex]T=12+20+38+20+10=100[/tex]Then, the condition 'a teenager has 4 or more pairs of shoes' is satisfied if the number of shoes is either 4 or 5; then,
[tex]P(4or5)=P(4)+P(5)=\frac{20}{100}+\frac{10}{100}=\frac{30}{100}=\frac{3}{10}[/tex]The exact answer is 3/10 or 0.3 (both are equivalent)The diagonales of this rhombus are 20 millimeters and 7 millimeters.
Answers
The rule of the area of the rhombus using its 2 diagonals is
[tex]A=\frac{d1\times d2}{2}[/tex]Since the diagonals of the given rhombus are 20 mm and 7 mm
Then d1 = 20 and d2 = 7
Substitute them in the rule above
[tex]\begin{gathered} A=\frac{20\times7}{2} \\ A=\frac{140}{2} \\ A=70mm^2 \end{gathered}[/tex]The area of the rhombus is 70 square millimeters
The lengths of two sides of an isosceles triangle are 5 and 9. The length of the third side could beA. 9, onlyB. none of theseC. either 5 or 9D. 5, only
Answers
Step 1: Theorem
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
Step 2: Given data
Two sides are given with lengths 5 and 9.
Step 3:
The two equal lengths can be 5 and 5 or 9 and 9
Step 4:
The third length can be 5 or 9.
Final answer
is either 5 or 9.
Which of the following is equal to √500? 5010√5010√550√105√10
Answers
You can use the product property of square roots:
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}[/tex]Also, you can express 500 as the product of 100*5, then
[tex]\begin{gathered} \sqrt[]{500}=\sqrt[]{100\cdot5}\text{ appling the product property} \\ \sqrt[]{100\cdot5}=\sqrt[]{100}\cdot\sqrt[]{5}\text{ and the square root of 100 is 10, then} \\ \sqrt[]{100}\cdot\sqrt[]{5}=10\cdot\sqrt[]{5} \end{gathered}[/tex]The answer is 10√5
A. Graph Cubas population and describe what pattern you can see. B. Explain why a logistic model would be a better choice for Cubas population growth than an exponential model. C. Find a logistic function f(t)= L/1+C(e^-bt), that models Cubas population growth. - Assume that .039 is a good value for b. Do not change this value - Graph f(t) = 11,000/1+15(e^-.039t) on top of your points (so starting value L=11,000 and the starting value for C=15) - experiment with values for L and C until you have a good model for the graphed points. Limit yourself to L-values between 11,000 and 15,000 and C-values between 11 and 15
Answers
A. We have to graph the data (years in the horizontal axis, population in the vertical axis):
B. The shape of the time series match the logisti model: it has an exponential growth in the first stage and then it flattens.
C. We have a logistic model with b=0.039.
We have to plot the function:
[tex]f\mleft(t\mright)=\frac{11000}{1+15\cdot e^{-0.039t}}[/tex]If we add it to the data plot we get:
This parameters do not fit the actual population. So we have to change L between 11000 and 15000 and C between 11 and 15.
If we change them to C=14 and L=13000, we get:
which is a significant better fit than the original model.
Find the equation of the line which passes through the points(-5,8) And is perpendicular to the given line express your answer in slope intercept form simplify your answer
Answers
Given: The equation below
[tex]4x+7y=4y-7[/tex]To Determine: The equation of the line that passes through the point (- 5, 8) and is perpendicular to the given equation
Solution
Let us determine the slope of the given equation
[tex]\begin{gathered} 4x+7y=4y-7 \\ 7y-4y=-4x-7 \\ 3y=-4x-7 \\ \frac{3y}{3}=\frac{-4x}{3}-\frac{7}{3} \\ y=-\frac{4}{3}x-\frac{7}{3} \end{gathered}[/tex]The slope-intercept form of a linear equation is given as
[tex]\begin{gathered} y=mx+c \\ m=slope \\ c=y-intercept \end{gathered}[/tex]Comparing the slope-intercept form to the given equation
[tex]\begin{gathered} y=-\frac{4}{3}x-\frac{7}{3} \\ y=mx+c \\ slope=m=-\frac{4}{3} \\ c=-\frac{7}{3} \end{gathered}[/tex]Note: If two lines are perpendicular to each other, the slope of one of the line is equal to the negative inverse of the other
Therefore, the slope of the perpendicular line is as shown below
[tex]\begin{gathered} slope(given-equation)=m \\ slope(perpendicular-line)m_2=-(m)^{-1} \\ So \\ m=-\frac{4}{3} \\ m_2=-(-\frac{4}{3})^{-1} \\ m_2=-(-\frac{3}{4}) \\ m_2=\frac{3}{4} \end{gathered}[/tex]If the perpendicular line passes through (-5,8), the equation of the line can be derived using the formula below
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=slope \\ (x_1,y_1)=(-5,8) \\ slope=\frac{3}{4} \\ Therefore, \\ \frac{y-8}{x--5}=\frac{3}{4} \end{gathered}[/tex][tex]\begin{gathered} \frac{y-8}{x+5}=\frac{3}{4} \\ y-8=\frac{3}{4}(x+5) \\ y-8=\frac{3}{4}x+\frac{15}{4} \\ y=\frac{3}{4}x+\frac{15}{4}+8 \end{gathered}[/tex][tex]\begin{gathered} y=\frac{3}{4}x+\frac{15+32}{4} \\ y=\frac{3}{4}x+\frac{47}{4} \end{gathered}[/tex]Hence, the equation of the line that passes through the point ( - 5, 8) and perpendicular to the given equation is
[tex]y=\frac{3}{4}x+\frac{47}{4}[/tex]While value of x is a solution to this equation? 5x^2-36x+36=0A. x=-6B. x=4C. x=-1.8D. x=1.2
Answers
Answer:
D. x = 1.2
Explanation:
A value of x is a solution of the equation if when we replace, x by the given value, the equation is satisfied.
Therefore, for each option we get:
A. Replacing x = -6, we get:
5x² - 36x + 36 = 0
5(-6)² - 36(-6) + 36 ≠ 0
5(36) + 216 + 36 ≠ 0
180 + 216 + 36 ≠ 0
432 ≠ 0
Then, x = -6 is not a solution of the equation
B. Replacing x = 4, we get:
5x² - 36x + 36 = 0
5(4)² - 36(4) + 36 ≠ 0
5(16) - 144 + 36 ≠ 0
80 - 144 + 36 ≠ 0
-28 ≠ 0
Then, x = 4 is not a solution of the equation
C. Replacing x = -1.8, we get:
5x² - 36x + 36 = 0
5(-1.8)² - 36(-1.8) + 36 ≠ 0
5(3.24) + 64.8 + 36 ≠ 0
16.2 + 64.8 + 36 ≠ 0
117 ≠ 0
Then, x = -1.8 is not a solution of the equation
D. Replacing x = 1.2, we get:
5x² - 36x + 36 = 0
5(1.2)² - 36(1.2) + 36 = 0
5(1.44) - 43.2 + 36 = 0
7.2 - 43.2 + 36 = 0
0 = 0
Then, x = 1.2 is a solution of the equation
Therefore, the answer is x = 1.2
JK bisects angle LJM, the measure of angle LJM=2x+15, and the measure of angle KJM=6x-5. Solve for x.
Answers
JK bisects angle LJM, the measure of angle LJM=2x+15, and the measure of angle KJM=6x-5. Solve for x.
In this problem we have that
because JK bisects angle LJM
substitute the given values
(2x+15)=2(6x-5)
solve for x
2x+15=12x-10
12x-2x=15+10
10x=25
x=25/10
x=2.5which of the following values is the solution of x divided by 32 equals 8?A. 24B.40C.256 D.4
Answers
If the domain of f(x) = 3x + 5 is {-1, 0, 1, 2, 3}, what is the range?
Answers
The domain is the set of values that are allowed to plug into our function and it is represented by the variabel x.. In our case, the domaini s {-1,0,1,2,3}. On the other hand, the range is the set of values that the function assumes after we plug an x value in.
Then, we need to substitute each x value into the given function f(x). So, for x=-1, we have
[tex]\begin{gathered} f(-1)=3(-1)+5 \\ f(-1)=-3+5 \\ f(-1)=2 \end{gathered}[/tex]Similarly, for x=0, we get
[tex]\begin{gathered} f(0)=3(0)+5 \\ f(0)=5 \end{gathered}[/tex]For x=1, we obtain
[tex]\begin{gathered} f(1)=3(1)+5 \\ f(1)=8 \end{gathered}[/tex]Now, for x=2, we have
[tex]\begin{gathered} f(2)=3(2)+5 \\ f(2)=11 \end{gathered}[/tex]and finally, for x=3 we get
[tex]\begin{gathered} f(3)=3(3)+5 \\ f(3)=14 \end{gathered}[/tex]Therefore, the range is the following set:
[tex]{}\lbrace2,5,8,11,14\rbrace[/tex]Which answer choice correctly represents 0.513333… ?A) 0.513 _B) 0.513 __C) 0.513 ___D) 0.513
Answers
Explanation
The given question is an example of a recurring decimal
The decimal number given:
[tex]0.513333\ldots\text{..}[/tex]This shows that 3 continues indefinitely
A good way to write this will be to put a sign on 3 to show that it continues
This will be
Thus, the answer is option B
a surveyor standing 58 M from the base of a building measures the angle to the top of the building and finds it to be 39 degrees. the surveyor then measures the angle to the top of the radio tower on the building and find that it is 48°. how tall is the radio tower .
Answers
First, let's calculate the height to the top of the building:
Thereby,
[tex]\begin{gathered} \tan 39=\frac{B}{58}\rightarrow B=58\tan 39 \\ \Rightarrow B=46.97m \end{gathered}[/tex]Now, let's calculate the height to the top of the radio tower:
This way,
[tex]\begin{gathered} \tan 48=\frac{T}{58}\rightarrow T=58\tan 48 \\ \Rightarrow T=64.42 \end{gathered}[/tex]Substracting both heights, we'll get that:
[tex]64.42-46.97=17.45[/tex]The radio tower is 17.45 m tall.
indicate me answer choice The spinner shown is spun once. Find each probability. Write each answer as a fraction, a decimal, and a percent. B E M C A P P(not M) Oa. 2 3 Da Į, N0.7,8 67% Ob. 0,17,8 17 Oc. 5, N 0.3, 33% Od. 3 0.83, 83%
Answers
When the spinner is spun,
Last year Brian opened an investment account with $5800. At the end of the year, the amount in the account had increased by 24.5%. How much is this increased in dollars? How much money was in his account at the end of last year?
Answers
Part a
How much is this increased in dollars?
Remember that
24.5%=24.5/100=0.245
so
Multiply the initial amount by the factor of 0.245, to obtain how much is increased
$5,800*0.245=$1,421
the answer part a is $1,421Part b
How much money was in his account at the end of last year?
Adds $5,800 and $1,421
$5,800+$1,421=$7,221
the answer part b is $7,221A man purchased a magazine at the airport for $2.39. The tax on the purchase was $0.17. What is the tax rate at the airport? Raund to the nearest percentThe tax rate is ? Round to the nearest percent as needed.
Answers
In order to find the percent corresponding to the tax rate, we divide the tax over the cost of the magazine and multiply it by 100
[tex]\frac{0.17}{2..39}\cdot100=7.11\text{\%}\approx7\text{\%}[/tex]Simplify.4(7d+9)28d + 3628d + 911d + 1311d + 9
Answers
To simplify the above expression, simply distribute "4" or multiply it to the numbers inside the parenthesis.
[tex]\begin{gathered} (4\times7d)+(4\times9) \\ 28d+36 \end{gathered}[/tex]Hence, the answer is 28d + 36.
Given the following table with selected values of f (x) and g(x), evaluate f (g(1)).x–6–4134f (x)4–1–613g(x)143–4–6A. –4B.–1C.1 D.4
Answers
[tex]f[g(1)][/tex]
The function is a composite function
Let us first find g(1)
[tex]g(1)=3[/tex]The problem now reduces to f(3)
[tex]f(3)=1[/tex]The final answer is 1 .
The right choice is OPTION C
Jonah's restaurant bill comes to $25.65 and he leaves a 15% tip. What is Jonah's total restaurant bill?
Answers
Given
Restaurante bill $ 25.65
Tip 15%
Total
Procedure
Total = 25.65 + 25.65*15%
Total = 25.65+3.847
Total = 29.4975
4. In a geometric sequence, ag = 64 and a 10 = 0.25.Use the geometric mean to find the value of ag.3216
Answers
We are asked to determine the term between the 8th and 10th terms of the geometric sequence. To do that we need to have into account that in a geometric sequence the term between two given terms is equivalent to the geometric mean of the two terms. The geometric terms between the two terms is given by:
[tex]G_m=\sqrt[]{a_1a_2}[/tex]Replacing the values:
[tex]\begin{gathered} G_m=\sqrt[]{(64)(0.25)}_{} \\ G_m=\sqrt[]{16} \\ G_m=4 \end{gathered}[/tex]Therefore, the 9th term is 4.
Solve the following system of equations using elimination. A. (4, 2)B. (2, 16)C. (-2, 16)D. (16, -2)
Answers
Answer:
A. (4, 2)
Explanation:
Given the system of equations:
[tex]\begin{gathered} x+3y=10\cdots(1) \\ 6x+12y=48\cdots(2) \end{gathered}[/tex]In order to use the elimination method, multiply the first equation by 6 to make the coefficients of x the same.
[tex]\begin{gathered} 6x+18y=60\cdots(3) \\ 6x+12y=48\cdots(2) \end{gathered}[/tex]Subtract equation (2) from equation (3).
[tex]\begin{gathered} 6y=12 \\ \text{Divide both sides by 6} \\ y=\frac{12}{6} \\ y=2 \end{gathered}[/tex]Next, solve for x using any of the equations:
[tex]\begin{gathered} x+3y=10 \\ x+3(2)=10 \\ x=10-6 \\ x=4 \end{gathered}[/tex]The solution to the system of equations is (x,y)=(4,2).
Option A is correct.
Solve for: A = a b= Round to the nearest tenth.
Answers
We have the following triangle:
First, we start from the fact that we have an internal angle of 72 degrees and a right angle i.e. a 90-degree angle.
Second, having two internal angles, we solve and find the last internal angle.
[tex]180-90-72=18[/tex]Third, we find "a" and "b" with the law of sines, the equation of this law is:
[tex]\frac{a}{\sin(A)}=\frac{b}{\sin (B)}=\frac{c}{sn(C)}[/tex]Where we have these values:
[tex]\begin{gathered} a=a \\ b=b \\ c=11 \\ \sin (A)=\sin (18) \\ \sin (B)=\sin (72) \\ \sin (C)=\sin (90)=1 \end{gathered}[/tex]Now we solve "a"
[tex]\begin{gathered} \frac{a}{\sin (18)}=\frac{11}{\sin (90)} \\ a=11\cdot\sin (18) \\ a=3.3991\cong3.4 \end{gathered}[/tex]Now we solve "b"
[tex]\begin{gathered} \frac{b}{\sin (72)}=\frac{11}{\sin (90)} \\ b=11\cdot\sin (72) \\ b=10.4646\cong10.46 \end{gathered}[/tex]In conclusion, the answers are approximate:
[tex]\begin{gathered} a\cong3.4 \\ b\cong10.46 \end{gathered}[/tex]At the fair 220 balloons are given to 40 children, 3/4 of whom are girls. Each boy receives twice as many balloons as each girl. How many more balloons do all the girl receive than all the boys
Answers
We have the following:
3/4 of 40 = 30 girls, therefore 10 boys
Due each boy receives twice as many balloons as each girl
boys get a multiple of 20 balloons (10 * 2), girls get the same multiple of 30 (30 * 1) balloons.
so
x * (30 + 20) = 220 balloons
x * 50 = 220 balloons
x = 220/50
so the number is 4.4
Boys receive 20 * 4.4 = 88 balloons.
Girls receive 30 * 4.4 = 132 balloons.
Write 0.611111111111 as a fraction PLEASE EXPLAIN STEP BY STEP!
Answers
We have to write N=0.6111... as a fraction.
This is a periodic number.
We start by transforming the number as:
[tex]10\cdot N=10\cdot0.6111\ldots=6.111\ldots=6+0.111\ldots[/tex]Now we take the periodic part we have (x=0.111...) and express it like this:
[tex]10x=10\cdot0.111\ldots=1.111\ldots=1+0.111\ldots=1+x[/tex]Then, we have:
[tex]\begin{gathered} 10x=1+x \\ 10x-x=1 \\ 9x=1 \\ x=\frac{1}{9} \end{gathered}[/tex]We use 10 to have the non-periodic part as an integer and the periodic part as a decimal.
Now we know that our periodic part of the number is equal to 1/9.
So we come back to N and complete:
[tex]\begin{gathered} 10N=6+0.111\ldots=6+\frac{1}{9} \\ N=\frac{1}{10}(6+\frac{1}{9})=\frac{1}{10}(\frac{6\cdot9}{9}+\frac{1}{9})=\frac{1}{10}\cdot\frac{54+1}{9}=\frac{1}{10}\cdot\frac{55}{9}=\frac{55}{90} \end{gathered}[/tex]Then, 0.6111... as a fraction is 55/90.
Can I please get help on this question I guessed it and I got it right. But I would like to know the solution to this.
Answers
Remember that, the Confidence Interval is a range of estimates defined by a lower bound and an upper bound. The larger the percentage of the confidence interval is, the more data the CI range includes.
Therefore, the 95% interval contains more data than the 90% confidence interval. Then, the answer is always narrower.
The probability that a customer will order a nonalcoholic beverage is .48b. Find the probability that in a sample of 12 customers, at least 5 will order a nonalcoholic beverage. (Round your answer to 4decimal places.)
Answers
Given:
probability of ordering non-alcoholic beverage = 0.48
probability of not ordering non-alcoholic beverage = 1 - 0.48 = 0.52
FInd: the probability that in a sample of 12 customers, at least 5 will order a nonalcoholic beverage.
Solution:
Recall the binomial probability formula.
[tex]P(x)=nCr\times p^r\times q^{n-r}[/tex]where
p = probability of success: 0.48
q = probability of failure: 0.52
n = the number of samples: 12
r = number of success (at least 5 which means not 1, 2, 3, or 4.
To determine the probability of having at least 5, let's calculate when r = 0, r = 1, r = 2, r = 3, and r = 4.
Let's start with r = 0 and solve.
[tex]P(0)=_{12}C_0\times0.48^0\times0.52^{12}[/tex][tex]\begin{gathered} P(0)=1\times1\times0.000390877 \\ P(0)=0.000390877 \end{gathered}[/tex]At r = 1,
[tex]P(1)=_{12}C_1\times0.48^1\times0.52^{11}[/tex][tex]\begin{gathered} P(1)=12\times0.48^\times0.000751686 \\ P(1)=0.0043297 \end{gathered}[/tex]Now, let's solve for r = 2.
[tex]P(2)=_{12}C_2\times.48^2\times.52^{10}[/tex][tex]\begin{gathered} P(2)=66\times.2304\times.00144555 \\ P(2)=0.02198 \end{gathered}[/tex]Moving on to r = 3.
[tex]P(3)=_{12}C_3\times0.48^3\times0.52^9[/tex][tex]\begin{gathered} P(3)=220\times0.110592\times0.0027799 \\ P(3)=0.067636 \end{gathered}[/tex]Then, lastly at r = 4.
[tex]P(4)=_{12}C_4\times0.48^4\times0.52^8[/tex][tex]\begin{gathered} P(4)=495\times0.05308\times0.00534597 \\ P(4)=0.14047 \end{gathered}[/tex]Let's now add the probability of getting r = 0, r = 1, r = 2, r =3, and r = 4 customers ordering a nonalcoholic beverage.
[tex]P(0)+P(1)+P(2)+P(3)+P(4)[/tex][tex]0.0043297+0.02198+0.067636+0.14047=0.2344157[/tex][tex]0.000390877+0.0043297+0.02198+0.067636+0.14047=0.2348[/tex]0.2348 is the probability of at most 4 customers ordering a non-alcoholic beverage.
Since the question is the probability of at least 5 customers ordering a non-alcoholic beverage which is the opposite of the at most 4 customers, then, let's subtract its probability from 1.
[tex]1-0.2348=0.7652[/tex]Therefore, the probability that in a sample of 12 customers, at least 5 will order a nonalcoholic beverage is approximately 0.7652.