Answer:
Step-by-step explanation:
The mean of the reading points is
Mean = (5.8 + 5.9 + 4.9 + 5.2 + 5.0 + 4.9 + 6.2 + 5.1 + 5.7 + 6.1)/10 = 5.48
The process is out of control if the mean salt level of the readings is greater than 5.4
For the null hypothesis,
µ = 5.4
For the alternative hypothesis,
µ > 5.4
This is a right tailed test.
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 5.4
x = 5.48
σ = 0.3
n = 10
z = (5.48 - 5.4)/(0.3/√10) = 0.84
Looking at the normal distribution table, the probability corresponding to the z score is 0.7996
The probability value to the right of the z score is 1 - 0.7996 = 0.2
Assuming a significance level of 0.05
Since alpha, 0.05 < than the p value, 0.2, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the process is not out of control. If we had rejected the null hypothesis, then our conclusion would be that the process is out of control.
A line has a slope of -
Which ordered pairs could be points on a line that is perpendicular to this line? Select
Which ordered pairs coul
two options
Answer:
(a) -2,0 and 2,5 and (b) 2,-1 and 10,9
Question:
The question is incomplete without the answer choice. Let's consider the following:
A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? select two options
a) -2,0 and 2,5
b) -4,5 and 4,-5
c) -3,4 and 2,0
d) 1,-1 and 6,-5
e) 2,-1 and 10,9
Step-by-step explanation:
The ordered pairs that could be points on a line that is perpendicular to this line would have same slope as that of the line.
Let's check out the slope of the options.
The line has slope = -4/5
Slope = m = (y subscript 2 -y subscript 1)/(x subscript 2 - x subscript 1)
The coordinates is in the form of (x,y)
Find attached the workings.
a) -2,0 and 2,5
m = 5/4
b) -4,5 and 4,-5
m = -5/4
c) -3,4 and 2,0
m = -4/5
d) 1,-1 and 6,-5
m = -4/5
e) 2,-1 and 10,9
m = 5/4
Two lines are perpendicular if (m subscript 1) × (m subscript 2) = -1
In other words, the slopes
of the two lines must be negative reciprocals of each other.
If 1st slope = -4/5
For the lines to be perpendicular, the slope of every other line = 5/4
2nd slope = 5/4
The ordered pairs that are points on the line perpendicular to the line:
(a) -2,0 and 2,5 and (b) 2,-1 and 10,9
Answer:AandE
Step-by-step explanation:
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
1/2
Step-by-step explanation:
Find two points on the line
(2,0) and (4,1)
The slope is given by
m= (y2-y1)/(x2-x1)
=(1-0)/(4-2)
= 1/2
A bag contains red and blue marbles, such that the probability of drawing a blue marble is an experiment consists of drawing a
marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue
marbles to each outcome
What is the range of the random variable?
{1,2,3}
{6,7,8)
b. {0,1,2)
d {8, 9, 10
a
С.
Please select the best answer from the choices provided
OOOO
C
Mark this and return
Save and Exit
Next
Submit
Answer:
The range of the random variable is {0, 1, 2}.
Step-by-step explanation:
The bag contains red and blue marbles.
The experiments consists of two draws, with reposition.
The random variable assigns the number of blue marbles to each outcome.
If we have only two draws, we can only get 0, 1 or 2 blue marbles.
The range of the random variable is {0, 1, 2}.
Find the lengths of the 2 Missing sides of each triangle
Green
x=14.7
y=8.5
Red
x=3.5
y=6
Mrs Van Roijen decides to abseil down the Shard in London. The journey down normally takes 33 minutes. However, on her way down, she stops for 18 minutes to take some photos. Eventually she arrives at the bottom of the Shard. Looking at her watch she sees that it is now 12:15. At what time did she set off? 11: 34
11: 24
11: 44
11: 54
Answer:
11.24
Step-by-step explanation:
If she arrived at 12.15, to find the time of departure we have to deduct 33 mins and the time she spent for photos,18 mins from this to get time of departure.
Total time spent for journey
33mins +18 mins = 51mins
time of departure = 12.15 - 51mins
so the time of departure is 11.24
what is the volume of aright square prism whose length of side of the base is 6cm and height 10cm?
Answer: 360 cubic centimeters.
Step-by-step explanation:
Since it has a base shaped like a square and we know that it has a side length of 6 cm then we could square it an multiply it by the height.
6^2 = 36
36 * 10 = 360
The circular area covered by a cell phone tower can be represented by the expression 225π miles2. What is the approximate length of the diameter of this circular area
Answer:
The length of the diameter of this circular area is of 30 miles.
Step-by-step explanation:
The area of a circular region can be represented by the following equation:
[tex]A = \pi r^{2}[/tex]
In which r is the radius. The diameter is twice the radius.
In this question:
[tex]A = 225\pi[/tex]
So
[tex]A = \pi r^{2}[/tex]
[tex]225\pi = \pi r^{2}[/tex]
[tex]r^{2} = 225[/tex]
[tex]r = \pm \sqrt{225}[/tex]
The radius is a positive measure, so
[tex]r = 15[/tex]
Area in squared miles, so the radius in miles.
What is the approximate length of the diameter of this circular area
D = 2r = 2*15 = 30 miles
The length of the diameter of this circular area is of 30 miles.
Classify the triangle by its sides, and then by its angles.
6 in.
8 in.
10 in.
Classified by its sides, the triangle is a(n)
▼
isosceles
scalene
equilateral
triangle.
Classified by its angles, the triangle is a(n)
▼
acute
obtuse
right
triangle.
Answer: scalene and right
Step-by-step explanation:
You get tired of the sand and head up to the amusement park. You can purchase 20 ride tickets for $14 or you can purchase 30 ride tickets for $22.50. Which is a better deal?
Answer:
The one with the better deal would be 30 ride tickets for $22.50 this is because you pay less money for more rides.
Step-by-step explanation:
First you divide 20 by 14. Doing this will give you the cost of a ride per ticket.
20/14 = 1.42
Then you do the same thing to 30 and 22.50.
30/22.50 = 1.30
Last you compare which deal has less money per ride.
1.42 > 1.30
Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
y= -7x+3
y = -x-3
Answer: The answer has one solution:
_______________________________
→ x = 1 ; y = -4 ; or, write as: [1, -4].
_______________________________
Step-by-step explanation:
_______________________________
Given:
y = - 1x – 3
y = -7x + 3 ;
_______________________________
-1x – 3 = -7x + 3 ; Solve for "x" ;
Add: " +1x" ; and add " +3 " ; to Each Side of the equation:
Subtract " 1x " ; and Subtract " 1 " ; from Each Side of the equation:
-1x + 1x – 3 + 3 = -7x + 1x + 3 + 3 ;
to get:
0 = -6x + 6
↔ -6x + 6 = 0 ;
Now, subtract " 6 " from Each Side of the equation:
-6x + 6 – 6 = 0 – 6 ;
to get:
-6x = -6 ;
Now, divide Each Side of the equation by " -6 ";
to isolate "x" on one side of the equation;
& to solve for "x" ;
-6x /-6 = -6/-6 ;
to get:
x = 1 .
_______________________________
Now, let us solve for "y" ;
We are given:
y = -x – 3 ;
Substitute our solved value for "x" ; which is: " 1 " ; for " x " ; into this given equation; to obtain the value for " y " :
y = -x – 3 ;
= -1 – 3
y = - 4 .
_______________________________
Let us check our answers by plugging the values for "x" and "y" ;
" 1 " ; and " -4 "; respectively); into the second given equation; to see if these values for " x " and " y" ; hold true:
Given: y = - 7x + 3 ;
→ -4 =? -7(1) + 3 ?? ;
→ -4 =? -7 + 3 ?? ;
→ - 4 =? -4 ?? ;
→ Yes!
_______________________________
The answer has one solution:
→ x = 1 ; y = - 4 ; or, write as: [1, -4 ].
_______________________________
Hope this is helpful! Best wishes!
_______________________________
Which is equivalent to 8−+3
8
x
-
y
+
3
x
?
Answer:
DIDNT UNDERSTAND THE QUESTION PROPERLY BRO..
KEEP THE QUESTION AGAIN
Solve for x in the diagram below
Answer:
So the diagram couldn't come due to coronavirus?
Answer:
there is no diagram
Step-by-step explanation:
When a feasible region is bounded on all sides, where will the maximum and minimum values of the objective function occur?
at the center of the feasible region
at the top of the feasible region
anywhere within the feasible region
at the vertices of the feasible region
Answer:
Option 4: at the vertices of the feasible region.
I completed the quiz
Answer:
at the vertices of the feasible region
Step-by-step explanation:
this is the correct answer
hope i helped
~Help me with this please I will mark as BRANLIEST and give you 55 POINTS! (If you answer correctly)
Answer:
[tex]y=50x+75[/tex]
Step-by-step explanation:
When writing a linear equation from a graph, we need to find two things: the y-intercept (what y is when x is 0) and the slope.
First, let us find the y-intercept.
To do this, we can just look at the graph. When x=0, y=75, so 75 is our y-intercept, which is also known as b.
To find the slope of this line, we will need to look at two points
We already know that (0,75) is a point. From the graph, we can see that (1,125) is also a point on this line.
Now, we can find the slope of this line using the following formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{125-75}{1-0} \\\\m=\frac{50}{1} \\\\m=50[/tex]
Now that we have both the y-intercept and slope, we can put them together in the form of [tex]y=mx+b[/tex]
[tex]y=50x+75[/tex]
Answer:
Slope: 50
Equation: y = 50x + 75
Step-by-step explanation:
Take two points:
(2,175)
(3,225)
Find the slope:
225 - 175/3 - 2
50/1 = 50
So we get this equation:
y = 50x + b
Now to find b, insert one of those points from before back in:
175 = 50(2) + b
175 = 100 + b
b = 75
So the equation is:
y = 50x + 75
help!! Algebra 1!!
sorry if the picture is bad
Answer:
The first one matches with f(x)√x because a square root cannot be negative
The second one matches with f(x)=√(x-5) because the square root would be negative if it were less than five.
The third one matches with f(x)=8x because there is nothing that makes it a not possible answer
The last one matches with 7/(x-8) because there cannot be a denominator of zero.
A service club is organizing a concert to raise funds for a retirement home. The club determines that the revenue from the concert can
be represented by R(x) = 0.0027x3 - 125, where x is the number of tickets sold. The cost to put on the concert is represented by the
function C(X) = 21x + 11,305.
Which of the following functions describes the funds raised, F(x), as a function of the number of tickets sold?
FX) = 0.0027x3 - 21x - 11,430
FAX) = 0.0027x3 + 21x - 11,180
FX) = 0.0027x3 - 21x - 11,180
F(X) = 0.0027x3+
+ 21-11,430
Answer:
maybe is a
Step-by-step explanation:
Answer:
F(x) = 0.0027x^3 - 21X - 11,430
Step-by-step explanation:
simplify (6 1/4)^4
a. 6^4
b. 1/6
c. 6^16
d. 6
Answer:
D not sure if its right tho
Answer:6
Step-by-step explanation:
Ten teaching assistants are available for grading papers in a particular course. The first exam consists of four questions, and the professor wishes to select a different assistant to grade each question (only one assistant per question). In how many ways can assistants be chosen to grade the exam
Answer:
There are 210 ways
Step-by-step explanation:
The number of ways or combinations in which we can select x elements from a group of n elements where the order doesn't matter can be calculated as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, we have 10 teaching assistants and we need to choose 4 (one assistant per question) to grade each question. It means that n is equal to 10 and x is equal to 4.
Therefore, the number of ways that the assistants can be chosen to grade the exam are calculated as:
[tex]10C4=\frac{10!}{4!(10-4)!}=210[/tex]
What equation results from completing the square and then factoring? x^2+2x=9
a. (x+2)^2=8
b. (x+1)^2=8
c.(x+1)^2=10
d.(x+2)^2=10
Answer:
c.(x+1)^2=10
Step-by-step explanation:
Completing the square:
We use the following relation:
[tex](x + a)^{2} = x^{2} + 2ax + a^{2}[/tex]
In this question:
[tex](x + a)^{2} = x^{2} + 2ax + a^{2} = x^{2} + 2x + a^{2}[/tex]
We have to find a.
[tex]2a = 2[/tex]
[tex]a = \frac{2}{2}[/tex]
[tex]a = 1[/tex]
[tex]x^{2} + 2x + 1 = (x+1)^{2}[/tex]
Thus, we have to add 1 on the right side of the equality.
We end up with:
[tex](x+1)^{2} = 9 + 1[/tex]
[tex](x+1)^{2} = 10[/tex]
So the correct answer is:
c.(x+1)^2=10
Find the area of a circle with radius, r = 17cm.
Give your answer rounded to 3 SF. (SF means Significant figures)
Answer:
0.0908 [tex]m^{2}[/tex] (to 3 S.F.)
Step-by-step explanation:
Area = π[tex]r^{2}[/tex]
π * [tex]17^{2}[/tex] = 907.92
= 908 [tex]cm^{2}[/tex]
=0.0908 [tex]m^{2}[/tex]
There are 4 blue tiles, 12 red tiles, and 6 green tiles in a bag. Which model represents the probability, P, that Luke will pick a red tile from the bag?
Answer:
The Probability that will pick a red tile from the bag
[tex]P(E) = \frac{6}{11}[/tex] = 0.545
Step-by-step explanation:
Explanation:-
Given data 4 blue tiles, 12 red tiles, and 6 green tiles in a bag
Total = 4 B + 12 R + 6 G = 22 tiles
Total number of exhaustive cases
n (S) = [tex]22 C_{1} = 22 ways[/tex]
The Probability that will pick a red tile from the bag
[tex]P(E) = \frac{n(E)}{n(S)} = \frac{12 C_{1} }{22 C_{1} } = \frac{12}{22}[/tex]
[tex]P(E) = \frac{6}{11}[/tex]
P(E) = 0.545
Final answer:-
The Probability that will pick a red tile from the bag = 0.545
In a manufacturing process, a machine produces bolts that have an average length of 5 inches with a variance of .08. If we randomly select five bolts from this process, what is the standard deviation of the sampling distribution of the sample mean
Answer:
[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})[/tex]
And replacing:
[tex] \mu_{\bar X}= 5[/tex]
And the deviation:
[tex] \sigma_{\bar X}= \frac{0.283}{\sqrt{5}}= 0.126[/tex]
And the distribution is given:
[tex] \bar X \sim N(\mu= 0.08, \sigma= 0.126)[/tex]
Step-by-step explanation:
For this case we have the following info given :
[tex] \mu= 5. \sigma^2 =0.08[/tex]
And the deviation would be [tex] \sigma = \sqrt{0.08}= 0.283[/tex]
For this case we select a sample size of n = 5 and the distirbution for the sample mean would be:
[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})[/tex]
And replacing:
[tex] \mu_{\bar X}= 5[/tex]
And the deviation:
[tex] \sigma_{\bar X}= \frac{0.283}{\sqrt{5}}= 0.126[/tex]
And the distribution is given:
[tex] \bar X \sim N(\mu= 0.08, \sigma= 0.126)[/tex]
A company manager for a tire manufacturer is in charge of making sure there is the least amount of defective tires. If the tire manufacturing process is working properly, the average weight of a tire for a 4-door sedan is normally distributed with a mean of 22 pounds and a standard deviation of 0.76 pounds. The manager decides to reject a tire as underweight if it falls more than 1.5 interquartile ranges below the lower quartile of the specified shipment of tires. What proportion of tires will be rejected by this process?
Answer:
0.347% of the total tires will be rejected as underweight.
Step-by-step explanation:
For a standard normal distribution, (with mean 0 and standard deviation 1), the lower and upper quartiles are located at -0.67448 and +0.67448 respectively. Thus the interquartile range (IQR) is 1.34896.
And the manager decides to reject a tire as underweight if it falls more than 1.5 interquartile ranges below the lower quartile of the specified shipment of tires.
1.5 of the Interquartile range = 1.5 × 1.34896 = 2.02344
1.5 of the interquartile range below the lower quartile = (lower quartile) - (1.5 of Interquartile range) = -0.67448 - 2.02344 = -2.69792
The proportion of tires that will fall 1.5 of the interquartile range below the lower quartile = P(x < -2.69792) ≈ P(x < -2.70)
Using data from the normal distribution table
P(x < -2.70) = 0.00347 = 0.347% of the total tires will be rejected as underweight
Hope this Helps!!!
The proportion of the tires that would be denied for being underweight through the given process would be:
[tex]0.347[/tex]% of the total tires will be rejected as underweight.
Given that,
Interquartile Range [tex]= 1.5[/tex]
Standard Deviation [tex]= 0.76[/tex]
Considering Mean = 0
and Standard Deviation = 1
Since lower quartile = -0.67448
Upper quartile = +0.67448
IQ range = 1.34896
To find,
The proportion of tires would be rejected due to being underweight through the process would be:
1.5 of Interquartile Range = 1.5 × [tex]1.34896 = 2.02344[/tex]
Now,
1.5 of the IQ range below the lower quartile [tex]= (lower quartile) - (1.5 of Interquartile range)[/tex]
[tex]= -0.67448 - 2.02344[/tex]
[tex]= -2.69792[/tex]
The proportion of tires that would be under 1.5 of the interquartile range below the lower quartile:
[tex]= P(x < -2.69792)[/tex] ≈ [tex]P(x < -2.70)[/tex]
Using data through the Normal Distribution Table,
[tex]P(x < -2.70)[/tex] [tex]= 0.00347[/tex]
[tex]= 0.347[/tex]%
Thus, 0.347% of the total tires would be rejected as underweight.
Learn more about "Proportion" here:
brainly.com/question/2548537
What’s the correct answer for this question?
Answer:
3724 in^3
Step-by-step explanation:
19 times 14 times 14 = 3724
Answer:
3724 inches ³
Step-by-step explanation:
Volume of cooler = whl
Where w is width, h is height and l is length
V = (19)(14)(14)
V = 3724 inches³
If the inter-quartile range is the distance between the first and third quartiles, then the inter-decile range is the distance between the first and ninth decile. (Deciles divide a distribution into ten equal parts.) If IQ is normally distributed with a mean of 100 and a standard deviation of 16, what is the inter-decile range of IQ
Answer:
The inter-decile range of IQ is 40.96.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 100, \sigma = 16[/tex]
First decile:
100/10 = 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 100}{16}[/tex]
[tex]X - 100 = -1.28*16[/tex]
[tex]X = 79.52[/tex]
Ninth decile:
9*(100/10) = 90th percentile, which is X when Z has a pvalue of 0.9. So it is X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 100}{16}[/tex]
[tex]X - 100 = 1.28*16[/tex]
[tex]X = 120.48[/tex]
Interdecile range:
120.48 - 79.52 = 40.96
The inter-decile range of IQ is 40.96.
A ball is thrown downward from the top of a 240-foot building with an initial velocity of 20 feet per second. The height of the ball h in feet after t seconds is given by the equation h= -16t^2 - 20t + 240. How long after the ball is thrown will it strike the ground?
Answer:
3.29 s
Step-by-step explanation:
We are given that
Height of building=240
Initial velocity=20ft/s
The height of the ball after t seconds is given by
[tex]h(t)=-16t^2-20t+240[/tex]
When the ball strike the ground then
h(t)=0
[tex]-16t^2-20t+240=0[/tex]
[tex]4t^2+5t-60=0[/tex]
Quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Using the quadratic formula
[tex]t=\frac{-5\pm\sqrt{25+960}}{8}[/tex]
[tex]t=\frac{-5\pm\sqrt{985}}{8}[/tex]
[tex]t=\frac{-5+31.28}{8}=3.29 s[/tex]
[tex]t=\frac{-5-31.38}{8}=-4.5[/tex]
Time cannot be negative .Therefore,
t=3.29 s
The table represents an exponential function. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 0.25, 0.125, 0.0625, 0.03125. What is the multiplicative rate of change of the function? 0.2 0.25 0.5 0.75
Answer:
0.5 or C on edge2021
Step-by-step explanation:
The multiplicative rate of change of the function will be:
0.5What is a Multiplicative rate of change?The multiplicative rate of change is the common factor that the numbers can be multiplied with to get the succeeding figures.
For instance, if 0.25 is multiplied by 0.5, the result will be 0.125. Also, if 0.125 is multiplied by 0.5, the result will be 0.0625.
Learn more about the multiplicative rate of change here:
https://brainly.com/question/4319809
#SPJ9
The graph shows the amount of protein contain in a certain brand of peanut butter. Which statement describes the meaning of the point (6, 30) on the graph?
A.) There are 6 g of protein per tablespoon of peanut butter.
B.) There are 30 g of protein per tablespoon of peanut butter.
C.) There is 6 g of protein in 30 tablespoons of peanut butter.
D.) There are 30 g of protein in 6 tablespoons of peanut butter.
Answer:
D.) There are 30 g of protein in 6 tablespoons of peanut butter.
Step-by-step explanation:
Interpretation of the graph:
x-axis: tablespoons
y-axis: grams of protein.
Which statement describes the meaning of the point (6, 30) on the graph?
(6,30) means that x = 6 and y = 30.
This means that in 6 tablespoons there are 30g of protein.
So the correct answer is:
D.) There are 30 g of protein in 6 tablespoons of peanut butter.
Answer:
The answer is D
f(x)= 2x^3- x^2 +x+ 1 is divided by 2x +1.
Answer:
Step-by-step explanation:
x^2
--------------------------------------------------
2x + 1 / 2x^3 - x^2 + x + 1
2x^3 + x^2
-----------------------
0 + x + 1
x + 1
The quotient is x^2 + ------------
2x + 1
A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes. A random sample of twelve service calls is taken. What is the probability that exactly eight of them take more than 93.6 minutes
Answer:
The probability that exactly eight of them take more than 93.6 minutes is 5.6015 [tex]\times 10^{-6}[/tex] .
Step-by-step explanation:
We are given that it is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes.
A random sample of twelve service calls is taken.
So, firstly we will find the probability that service calls take more than 93.6 minutes.
Let X = times for service calls.
So, X ~ Normal([tex]\mu=75,\sigma^{2} =15^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time = 75 minutes
[tex]\sigma[/tex] = standard deviation = 15 minutes
Now, the probability that service calls take more than 93.6 minutes is given by = P(X > 93.6 minutes)
P(X > 93.6 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{93.6-75}{15}[/tex] ) = P(Z > 1.24) = 1 - P(Z [tex]\leq[/tex] 1.24)
= 1 - 0.8925 = 0.1075
The above probability is calculated by looking at the value of x = 1.24 in the z table which has an area of 0.8925.
Now, we will use the binomial distribution to find the probability that exactly eight of them take more than 93.6 minutes, that is;
[tex]P(Y = y) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; y = 0,1,2,3,.........[/tex]
where, n = number of trials (samples) taken = 12 service calls
r = number of success = exactly 8
p = probability of success which in our question is probability that
it takes more than 93.6 minutes, i.e. p = 0.1075.
Let Y = Number of service calls which takes more than 93.6 minutes
So, Y ~ Binom(n = 12, p = 0.1075)
Now, the probability that exactly eight of them take more than 93.6 minutes is given by = P(Y = 8)
P(Y = 8) = [tex]\binom{12}{8}\times 0.1075^{8} \times (1-0.1075)^{12-8}[/tex]
= [tex]495 \times 0.1075^{8} \times 0.8925^{4}[/tex]
= 5.6015 [tex]\times 10^{-6}[/tex] .
