Tatooine is a fictional desert planet that appears in the Star Wars franchise. It is home to many settlers, including humans. Let X = weight of a human inhabitant on Tatooine. You know from prior research that X is approximately Normally distributed with population mean u = 96kg and population standard deviation o = 23.3kg. A. Specify the sampling distribution of statistic X, including stating what (5pts) type of distribution, its sampling mean uy, and its standard deviation Oy, for samples of 9 humans living on Tatooine. B. What is the Probability that a randomly selected group of 9 humans on (10pts) Tatooine would have a mean weight between 95 and 100kg? Include a rough sketch and Probability statement.

Answer:

38 + 10x + 4x - 2

14x + 36

answer is c

6x

Answer:

a) Chi square value = 1.031

b) There is no significant difference between the observed and expected values.

c) Check explanations for the part C of the question

Step-by-step explanation:

a) People away from work due to lower back injuries:

Observed value = 18

Expected value = 14.3

People away from work due to other injuries:

Observed value = 200 - 18 = 182

Expected value = 185.7

The chi square value is calculated by the formula:

[tex]x^{2} = \frac{(O-E)^{2} }{E}[/tex]

For people out of work due to lower back injuries:

Chi square value,

[tex]x^{2} = \frac{(18-14.3)^{2} }{14.3} \\x^{2} = 0.957[/tex]

For people out of work due to other injuries:

Chi square value,

[tex]x^{2} = \frac{(182-185.7)^{2} }{185.7} \\x^{2} = 0.074[/tex]

Total chi square value for the distribution:

[tex]x^{2} = 0.074 + 0.957\\x^{2} = 1.031[/tex]

b) The degree of freedom, df = n -1

n = 2 ( two categories of people are considered)

df = 2-1 = 1

For df = 1 and, chi square = 1.031

P - value = 0.3099

p- value = 0.3099, the result is not significant at p < 0.05

There is no significant difference between the observed and expected values.

c) Hypothesis testing helps the safety professionals to statistically analyse any situations and determine whether or not they are safe. It can help them to predict the outcome of a given situation by making necessary observations.

The question involves creating a network representation for multiple-source, multiple-destination distribution, for which nodes represent suppliers and counties, arcs represent the paths with capacities and costs, depicting the logistics of natural gas distribution by Tri-County Utilities, Inc.

Explanation:

The student is asking for a network representation for a supply and distribution problem faced by Tri-County Utilities, Inc. This is related to operations research within the business field, specifically dealing with the optimization of supply chain logistics. The company must distribute natural gas, supplied by Southern Gas and Northwest Gas, to three different counties with varying demand and distribution costs. The aim is to represent this scenario using a network graph that visualizes the routes between the suppliers (Southern Gas and Northwest Gas) and the counties (Hamilton, Butler, and Clermont) along with the distribution costs for each route.

To create a network representation, start with two nodes representing the suppliers and add three additional nodes representing the counties. Then, six directed arcs are drawn from the suppliers to the counties. The capacities of the arcs emanating from Southern Gas should be labeled with 500 units, and those from Northwest Gas should be labeled with 400 units. Likewise, the demand at each county node should be assigned (Hamilton with 400 units, Butler with 200 units, and Clermont with 300 units). Lastly, the costs should be labeled on each of the arcs as provided: from Southern Gas to Hamilton, Butler, and Clermont, the costs are 10, 20, and 15 (in thousands of dollars) respectively, and from Northwest Gas, the costs are 12, 15, and 18 (in thousands of dollars).

Final answer:

The detailed answer explains how to create a network representation for the gas supply problem.

Explanation:

Network Representation:

To develop a network representation of this problem, we can create a graph with nodes representing the counties and the suppliers, and edges representing the distribution costs per unit between them. Here's a simple representation:

Nodes: Hamilton County, Butler County, Clermont County, Southern Gas, Northwest Gas

Edges with Costs:

Hamilton County to Southern Gas - $10

Butler County to Southern Gas - $20

Clermont County to Southern Gas - $15

Hamilton County to Northwest Gas - $12

Butler County to Northwest Gas - $15

Clermont County to Northwest Gas - $18

Answer:

99.5% of all samples of 21 of​ today's women in their 20's have mean heights of at least 65.86 ​inches.

Step-by-step explanation:

We are given that a half-century ago, the mean height of women in a particular country in their 20's was 64.7 inches. Assume that the heights of​ today's women in their 20's are approximately normally distributed with a standard deviation of 2.07 inches.

Also, a samples of 21 of​ today's women in their 20's have been taken.

Let [tex]\bar X[/tex] = sample mean heights

The z-score probability distribution for sample mean is given by;

                          Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean height of women = 64.7 inches

            [tex]\sigma[/tex] = standard deviation = 2.07 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, Probability that the sample of 21 of​ today's women in their 20's have mean heights of at least 65.86 ​inches is given by = P([tex]\bar X[/tex] [tex]\geq[/tex] 65.86 inches)

  P([tex]\bar X[/tex] [tex]\geq[/tex] 65.86 inches) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{65.86-64.7}{\frac{2.07}{\sqrt{21} } }[/tex] ) = P(Z [tex]\geq[/tex] -2.57) = P(Z [tex]\leq[/tex] 2.57)

                                                                        = 0.99492  or  99.5%

The above probability is calculated by looking at the value of x = 2.57 in the z table which has an area of 0.99492.

Therefore, 99.5% of all samples of 21 of​ today's women in their 20's have mean heights of at least 65.86 ​inches.

Answer:

34 5/8

Step-by-step explanation:

you just add all the numbers on the left and the two drawer numbers then boom!!

Answer:

Please post another question with the angle that you were given. Thank you!

Step-by-step explanation:

There wasn't any angles given therefore, I couldn't help!

A function is a rule that assigns exactly one output to a given input. The input is taken from a set called the domain, and the corresponding output belongs to a set called the range.

1. In this exercise, we're calling the pool of patients 1-8 the domain, and the pool of nurses A-D the range. The given table describes a function because any patient is assigned to only one nurse.

2. This wouldn't be a function if at least one patient was assigned to more than one nurse. If this were to happen in practice, the patient could be, say, given the same dose of some medicine twice if the nurses aren't careful.

3. Making the nurse pool the domain and the patient pool the range would give a relation that is not a function, since more than one patient is assigned to one nurse.

Answer:

Your answer is 1341.75

Step-by-step explanation:

3/4 x 1440 = 1080

1080 + 295.25 = 1375.25

1375.25 + -33.50 = 1341.75

The solution of the given expression 3/4(1440) + 295.25 + (-33.50) involving multiplication, addition, and subtraction in mathematics is equal to 1341.75.

The expression provided is:

3/4(1440) + 295.25 + (-33.50)

To solve this, we need to follow the order of operations (PEMDAS):

Multiply 3/4 by 1440 to get 1080.

Add 1080 to 295.25 to get 1375.25.

Finally, subtract 33.50 from 1375.25 to get the final answer of 1341.75.

Answer:

48-15 is 33

Step-by-step explanation:

Answer:

The number of ways  to award the prizes if it satisfies the given conditions is 94,109,400.

Step-by-step explanation:

There are 100 tickets that are distributed among 100 different people.

Four different prizes are awarded, including a grand prize.

The selection of the four wining tickets can be done using permutations.

Permutation is an arrangement of all the data set in a specific order.

The formula to compute the permutation of k objects from n different objects is:

[tex]^{n}P_{k}=\frac{n!}{(n-k)!}[/tex]

In this case we need to compute the number of selection of the 4 winning tickets accordingly from 100 tickets.

Compute the number of ways to select 4 winning tickets as follows:

 [tex]^{n}P_{k}=\frac{n!}{(n-k)!}[/tex]

[tex]^{100}P_{4}=\frac{100!}{(100-4)!}[/tex]

         [tex]=\frac{100!}{96!}[/tex]

         [tex]=\frac{100\times99\times98\times97\times96!}{96!}[/tex]

         [tex]=94109400[/tex]

Thus, the number of ways  to award the prizes if it satisfies the given conditions is 94,109,400.

Answer:

Mean of sampling distribution = 25 inches

Standard deviation of sampling distribution = 4 inches

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 25 inches

Standard Deviation, σ = 12 inches

Sample size, n = 9

We are given that the distribution of length of the widgets is a bell shaped distribution that is a normal distribution.

a) Mean of the sampling distribution

The best approximator for the mean of the sampling distribution is the population mean itself.

Thus, we can write:

[tex]\bar{x} = \mu = 25\text{ inches}[/tex]

b) Standard deviation of the sampling distribution

[tex]s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{12}{\sqrt{9}} = 4\text{ inches}[/tex]

Using the Central Limit Theorem, it is found that:

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For the population:

Samples of size 9, thus [tex]n = 9[/tex].

By the Central Limit Theorem:

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The amount by which we must raise the price in order to retain your existing dollar profit margin is $2.04; the right solution is (a).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

There was a trucking strike that caused a prime ingredient in your menu item to shoot up by 17%. You were paying $12 per package.

The increases in the price of the ingredient = 17% of 12

Increase = 0.17 × 12            

Increase = 2.04

Therefore, the amount by which we must raise the price in order to retain your existing dollar profit margin is $2.04; the right solution is (a).

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The price of the menu item should be increased by $2.04.

Let's begin by calculating the new cost per package after the price increase. If the original cost per package was $12 and it increased by 17%, we calculate the increase as follows:

Increase = 12 * 0.17 = 2.04

The new cost per package will be:

New cost = 12 + 2.04 = 14.04

To maintain the same dollar profit margin on your menu item, you need to increase the price by the same amount as the cost increase, which is $2.04.

Answer:

•A c-chart is the appropriate control chart

• c' = 8.5

• Control limits, CL = 8.5

Lower control limits, LCL = 0

Upper control limits, UCL = 17.25

Step-by-step explanation:

A c chart is a quality control chart used for the number of flaws per unit.

Given:

Past inspection data:

Number of units= 100

Total flaws = 850

We now have:

c' = 850/100

= 8.5

Where CL = c' = 8.5

For control limits, we have:

CL = c'

UCL = c' + 3√c'

LCL = c' - 3√c'

The CL stands for the normal control limit, while the UCL and LCL are the upper and lower control limits respectively

Calculating the various control limits we have:

CL = c'

CL = 8.5

UCL = 8.5 + 3√8.5

= 17.25

LCL = 8.5 - 3√8.5

= -0.25

A negative LCL tend to be 0. Therefore,

LCL = 0

The appropriate control chart for the textile mill is the p-chart. The center line is 8.5 flaws per unit, and the control limits can be calculated using the formula LCL = p - Z * sqrt((p(1-p)) / n) and UCL = p + Z * sqrt((p(1-p)) / n).

The appropriate control chart for the textile mill to establish a control procedure on flaws in towels is the p-chart. This chart is used to monitor the proportion of defects in a process. The center line of the p-chart is calculated using the formula p = defects / units inspected. In this case, the center line is 850 / 100 = 8.5 flaws per unit. The control limits are calculated using the formula:

Where p is the proportion of defects, Z is the Z-score corresponding to the desired level of significance (such as 0.06), and n is the number of units inspected. The Z-score can be calculated using a Z-table or a statistical software. The control chart is used to determine if the process is in control or if there are any special causes of variation that need to be addressed.

Answer:

13.08

Step-by-step explanation:

The simplified result of the given mathematical expression (16 – 1.42 + (–1.5)) is 13.08. This is achieved by following the order of operations for addition and subtraction.

To answer this question, we need to simplify the given expression which includes subtraction and addition of numbers.

The expression is 16 – 1.42 + (–1.5). To simplify, we follow the order of operations, which for this question is just addition and subtraction from left to right.

First, subtract 1.42 from 16, which gives us 14.58.

Next, we need to add -1.5 to 14.58. When we add a negative number, it's the same as subtracting that number. Therefore, 14.58 - 1.5 = 13.08.

The simplified result of 16 – 1.42 + (–1.5) is 13.08.

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Answer: The inequality could be t > 900. Draw a number line so it includes 900. Draw an open circle on 900. Shade all the numbers greater than 900, or to the right.

Step-by-step explanation:

Inequality- Inequality is the something that is equal to the something or less than that of the sign give the conditions on which the graph is drawn on the basis of sales occured profits occured

Explanation to the above is the that mentioned below:

Thus we conclude that from the above the graph of the equation is solid line.

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Answer:

$226,300

Step-by-step explanation:

Given Allowance for Doubtful Accounts is estimated as $205,000 and Allowance for Doubtful Accounts has a debit balance of $21,300

#The  amount of the adjusting entry for uncollectible accounts is calculated as below:

[tex]Adjustment \ Cost=Allowance\ Doubtful\ Accounts +Doubtful \ Accounts \ Debit \ Balance\\\\=205000+21300\\\\\$226,300[/tex]

Hence,  the amount of the adjusting entry for uncollectible accounts is $226,300

Answer:

Equation: 10+c=3

Answer: c=-7

Step-by-step explanation:

1. 10+c=3

2. c=3-10

3. c=-7

Answer:

c=-7

Step-by-step explanation:

c+10=3

Subtract 10 from both sides

c=-7

Answer:

[tex]P(X=x)=0.0004928[/tex]

Step-by-step explanation:

-This is a binomial probability problem.

-Given the probability of catching a cold is 0.03, n=6

#The probability of exactly 3 people catching a cold is calculated as:

[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X=3)={6\choose3}0.03^3(1-0.03)^3\\\\=0.0004928[/tex]

Hence, the probability of exactly 3 in 6 people catching a cold is 0.0004928

The requried total cost of filling her three bottles with olive oil is 2250 x $0.0084 = $18.90.

Simplification is the process of using rules of arithmetic and algebra to eliminate extraneous terms, factors, or operations from an expression, with the objective of obtaining a more manageable, manipulable, or solvable expression. One approach to simplification involves combining like terms, factoring, or utilizing the distributive property when simplifying an algebraic expression.

Here,
Each bottle holds 0.75 liters, which is equivalent to 750 milliliters. So, Jane fills a total of 3 x 750 = 2250 milliliters of olive oil.

The cost of the olive oil is $0.21 for every 25 milliliters, which means the cost per milliliter is $0.21/25 = $0.0084.

Therefore, the total cost of filling her three bottles with olive oil is 2250 x $0.0084 = $18.90.

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It costs Jane $18.90 to fill her three bottles with olive oil, each holding 0.75 liters.

Calculating the Cost of Olive Oil

Jane has three bottles that each hold 0.75 liters. To find out how much it costs her to fill these bottles with olive oil, we need to make a few calculations.

Step-by-Step Calculation:

→ Total volume Jane needs:

= 3 bottles x 0.75 liters

= 2.25 liters

→ Convert liters to milliliters:

= 2.25 liters x 1000

= 2250 milliliters

→ Cost of 25 milliliters of oil: $0.21

→ Number of 25 milliliter increments in 2250 milliliters:

= 2250 / 25

= 90 increments

→ Total cost:

= 90 x $0.21

= $18.90

Therefore, it costs Jane $18.90 to fill her three bottles with olive oil.

Answer:

1/81

Step-by-step explanation:

P(1st ticket is a winner) = 1/9

These are independent events

P(2nd ticket is a winner) = 1/9

P (winner, winner) = 1/9 * 1/9 = 1/81

Answer:

161 inches

Step-by-step explanation:

This problem is all about conversion. How many feet are in a yard? 3. How many feet are in 4 yards? 12 feet. There are 12 inches in a foot. 12 feet means 12 x 12 inches, which is 144. 144 + the other 17 inches, is 161.

Answer:

The answer is into the unkown

Step-by-step explanation:

elsa and anna are good sisters olaf olaf anna fiftys ahdpnf3oehisklNHW3q3tsqagwgdraw4gw

Answer:

[tex]t=\frac{6.31-6}{\frac{1.2}{\sqrt{35}}}=1.5283[/tex]    

d. 1.5283

Step-by-step explanation:

Data given and notation    

[tex]\bar X=6.31[/tex] represent the sample mean    

[tex]s=1.2[/tex] represent the sample standard deviation    

[tex]n=35[/tex] sample size    

[tex]\mu_o =6[/tex] represent the value that we want to test    

t would represent the statistic (variable of interest)    

[tex]p_v[/tex] represent the p value for the test (variable of interest)    

State the null and alternative hypotheses.    

We need to conduct a hypothesis in order to check if the mean is higher than 6 seconds, the system of hypothesis are :    

Null hypothesis:[tex]\mu \leq 6[/tex]    

Alternative hypothesis:[tex]\mu > 6[/tex]    

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:    

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)    

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

Calculate the statistic    

We can replace in formula (1) the info given like this:    

[tex]t=\frac{6.31-6}{\frac{1.2}{\sqrt{35}}}=1.5283[/tex]    

d. 1.5283

In a one-sample t-test, the normal distribution of sample means is more important than the normality of individual data in the population. This follows the Central Limit Theorem which states that, with a decently large sample size, the distribution of sample means will approach normality regardless of the population distribution.

Statement C is the correct option. The Central Limit Theorem indicates that regardless of the population distribution, as long as we have a sufficiently large sample size, the sample means will be approximately normally distributed. However, this doesn't guarantee that the distribution of the individual data (the number of sleep hours) in the population is normal.

It’s important to note two things: First, the idea of random sampling is to avoid bias and to have a representative sample of the population under study. Second, the rule of thumb is that the sample size should be approximately 30 or greater for the Central Limit Theorem to take effect, to provide a decent approximation of a normal distribution of sample means. In this instance, a sample size of 20 is close to 30, so we may anticipate that the sample mean distribution is roughly normal.

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Answer:

The complete Python program to calculate the monthly payment on a loan with step by step explanation is given below.

Python Code with Explanation:

# get the loan amount from the user

LoanAmt=eval(input("Please enter the loan amount: "))

# get the annual interest rate from the user in percentage form

InterestRate=eval(input("Please enter the annual interest rate in percentage: "))

# get the number of months from the user

NumberMonths=eval(input("Please enter the number of months: "))

# convert the annual interest rate into monthly interest rate and also into decimal form according to the equation given in the question

MonthlyRate = InterestRate/1200

# implement the given equation to find out the required monthly payment, the operator (**) is used to raise to the power

Payment = (LoanAmt*MonthlyRate (1+MonthlyRate)**NumberMonths)/((1+MonthlyRate)**NumberMonths -1)

# finally, print the monthly payment

print("The monthly payment is: ", Payment)

Output:

Please enter the loan amount: 1500

Please enter the annual interest rate in percentage: 15

Please enter the number of months: 12

The monthly payment is: 135.38746851773584

Bonus:

You can use this command to limit the digits after the decimal point

For example following code will limit to 2 digits after the decimal point.

print(format(Payment, '.2f'))

Answer:

70

Step-by-step explanation: The sum of all interior angles in a triangle equal 180 degrees. Your problem already shows an angle of 90 degrees ( right angle) and an angle of 20 degrees.

180-90-20=70

Answer:

70°

Step-by-step explanation:

Every triangle's angles add to 180°

Therefore,

90+20=110

180-110=70°

Step-by-step explanation:

A rental car agency charges $30.00 per day  plus per mile $0.15.

Let x be the number of miles travelled by car

Their total cost = 30 + (0.15x)   ... (1)

Another rental car  agency charges $36.00 per day plus $0.10  per mile

Their total cost = 36 + (0.10x)   ... (2)

Equating (1) and (2), we get

30 + (0.15x) = 36 + (0.10x)

36 - 30 = 0.15x - 0.10x

6 = 0.05x

x = 120 miles

They should travel 120 mils in one day for both rental agencies  to cost the same amount to rent

Final answer:

To find the number of miles that would have to be driven in one day for both rental agencies to cost the same, set up an equation and solve for the number of miles ,  The two rental agencies would cost the same amount to rent if 120 miles were driven in one day.

Explanation:

Let's denote the number of miles driven in one day as x. The total cost for the first rental car agency would be $30.00 + $0.15x, and the total cost for the second agency would be $36.00 + $0.10x. In order for both rental agencies to cost the same amount, we can set up the equation:

$30.00 + $0.15x = $36.00 + $0.10x

Simplifying the equation, we get:

$0.05x = $6.00

Dividing both sides of the equation by $0.05, we find:

x = $120.00

Therefore, the two rental agencies would cost the same amount to rent if 120 miles were driven in one day.

Answer:

[tex]F(s) = \frac{s(e^{\pi s}+1)}{s^2 +1}[/tex]

Step-by-step explanation:

Using the formula for Laplace the transformations if [tex]F(s)[/tex]  is the converted function then

[tex]F(s) = \int\limits_{0}^{\infty} e^{-st} \cos(t) dt = \int\limits_{0}^{\pi} e^{-st} \cos(t) dt[/tex]

To solve that integral you need to use integration by parts, when you do integration by parts you get that

[tex]F(s) = \frac{s(e^{\pi s}+1)}{s^2 +1}[/tex].

Answer:

The laplace transform is [tex] F(s) = \frac{s(1+e^{-s\pi})}{s^2+1}[/tex]

Step-by-step explanation:

Let us asume that f(t) =0 for t<0. So, by definition, the laplace transform is given by:

[tex]I = \int_{0}^\pi e^{-st}\cos(t) dt[/tex]

To solve this integral, we will use integration by parts. Let u= cos(t)  and dv = [tex]e^{-st}[/tex], so v=[tex]\frac{-e^{st}}{s}[/tex] and du = -sin(t), then, in one step of the integration we have that

[tex]I = \left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi- \int_{0}^\pi \frac{\sin(t) e^{-st}}{s} dt[/tex]

Let [tex] I_2 = \int_{0}^\pi \frac{\sin(t) e^{-st}}{s} dt[/tex]. We will integrate I_2 again by parts. Choose u = sin(t) and dv = [tex]\frac{e^{-st}}{s}[/tex]. So

[tex] I_2 = \left.\frac{-\sin(t) e^{-st}}{s^2}\right|_{0}^\pi + \int_{0}^\pi \frac{\cos(t) e^{-st}}{s^2}dt [/tex]

Therefore,

[tex]I = \left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi - (\left.\frac{-\sin(t) e^{-st}}{s^2}\right|_{0}^\pi - \frac{1}{s^2} I[/tex]

which is an equation for the variabl I. Solving for I we have that

[tex]I(\frac{s^2+1}{s^2}) =\left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi+\left.\frac{\sin(t) e^{-st}}{s^2}\right|_{0}^\pi[/tex]

Then,

[tex]I = \left.\frac{-s\cos(t) e^{-st}}{s^2+1}\right|_{0}^\pi+\left.\frac{\sin(t) e^{-st}}{s^2+1}\right|_{0}^\pi[/tex].

Note that since the sine function is 0 at 0 and pi, we must only care on the first term. Then

[tex]I = \left.\frac{-s\cos(t) e^{-st}}{s^2+1}\right|_{0}^\pi = \frac{s}{s^2+1}(1-(-1)e^{-s\pi}} = \frac{s(1+e^{-s\pi})}{s^2+1}[/tex]

Answer:

(a) Find the probability of type I error. = 0.1018

Step-by-step explanation:

check attachment for the answer

Answer:

The probability of Type I error is = 0.10185.

Step-by-step explanation:

Solution:-

The type I - error is defined as the probability of rejecting Null hypothesis defined by Alternate hypothesis:

                          Ha : X ≥ 8

Where,

X : Denote the number of cars crash with no visible damage

The random variate "X" is defined by binomial distribution:

                            X ~ B ( n = 20 , p = 0.25 )

- The probability of Type I error:

                        P (Type I error ) = P ( Reject Null hypothesis )

                                                   = P ( X ≥ 8 )

- The probability mass function of binomial random variate "X" is given:

                     [tex]P ( X = x ) = nCr (p)^r * (1-p)^(^n^-^r^)\\P ( X \geq 8 ) = 1 - P ( X < 8 )\\\\P ( X \geq 8 ) = 1 - [ P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 ) + P ( X = 6 ) + P ( X = 7 ) ][/tex][tex]P ( X \geq 8 ) = 1 - [ (0.75)^2^0 + 20(0.25)*(0.75)^1^9 + 20C2(0.25)^2*(0.75)^1^8 +\\\\ 20C3(0.25)^3*(0.75)^1^7 + 20C4(0.25)^4*(0.75)^1^6 + 20C5(0.25)^5*(0.75)^1^5\\\\ + 20C6(0.25)^6*(0.75)^1^4 + 20C7(0.25)^7*(0.75)^1^3 ] \\\\\\P ( X \geq 8 ) = 1 - [ 0.00317 + 0.02114 + 0.06694 + 0.13389 + 0.18968 + 0.20233\\\\+ 0.16860 + 0.11240]\\\\P ( X \geq 8 ) = 1 - 0.89815 = 0.10185[/tex]

Answer: The probability of Type I error is = 0.10185.

The probability of getting a tail on the next coin flip remains at 50 percent, regardless of the previous series of outcomes because each coin flip is an independent event.

The question is concerned with the probability of getting a tail after having tossed a coin 100 times and obtaining 67 heads and 33 tails. Despite the past results of these tosses, the coin still has a 50 percent chance of landing on heads or tails on any given flip. This concept is based on the idea that each coin flip is an independent event with its own probability, unaffected by previous outcomes.

To answer the student's question directly, the probability that the next flip results in a tail is still 50 percent because past results do not change the probability of future coin flips. This is supported by the law of large numbers, which states that as the number of trials increases, the relative frequency of results will get closer to the expected probability.