Solved: 1. 4 boys and 3 girls are to be seated in a row of 7 chairs. How many ways can it be done under the following conditions: a. boys stay together? b. girls stay together? c. boys and girls are seated alternately? 2. Permute the letters of the word SAINT. How many permutations a. begin with vowels? b. end with consonants? c. begin with a vowel and end with a consonant? d. begin with a consonant and end with a vowel? 3. In how many ways can 4 people sit a round table if a. two people insist in sitting beside each other? b. two refuse to sit beside each other? c. one has a reserved seat?

A certain book manufacturing company presents the time it takes for sheets from a press to be folded, gathered, sewn, tipped on end sheets, and bound. The following data represent samples of books of two book production …

Find the 99th percentile of a normal curve

A Researcher surveyed 80 randomly selected Certified Public Accountants in each of the cities in Metro Manila area and asked them if they have performed work for free for 10 0r fewer clients in the last year. The results are shown in …

On the 3rd quarter examination in Statistics, the population mean was 70 and the population standard deviation was 9. Determine the standard score of a student who got a score of 88 assuming that the scores are normally distributed.

Find the 90th percentile of the normal curve

a. Determine the number of sets of all possible random samples that can be drawn from the given population by using formula,nCn,where N is the population size and n is the sample size.write your solutions in the box below.

On the 3rd quarter examination in Statistics, the population mean was 70 and the population standard deviation was 9. Determine the standard score of a student who got a score of 88 assuming that the scores are normally distributed.

A pair of fair dice is rolled. Let X be the random variable representing the sum of the numbers that appear. a. Construct the probability distribution of X for a pair of dice. b. Find P (X≥ 8). c…

A population consists of the values (1,3,5,7) consider a sample size of two that can be drawn from this population

Suppose a population consists of the numbers 2,3,5,8 and 12. What is the mean of the population? (Clue: Point Estimation)

1. Let X be a random variable that denotes the number of passengers in a train station for a given hour. What are the possible values of X?

Find the t_a/2 value for a 95% confidence interval when the sample size is 22.

examples of Functions (Continuity and inverse of a function),

In an intelligence test administered on 1000 children, the average was 60 and the standard deviation was 20. Assuming that the marks obtained by the children follow a normal distributed, find the number of children who have scored (i)…

a populatpion of 1,000 students has an average weekly allowance of =350 and standard deviation of =56.13 .what is the probability that a random sample of size =30 will have an average weekly allowance between 335 and 360?

Find the number of ways in which the word "BREAD' can be arranged when i) B and D take end places ii) E is placed in middle iii) vowels E and A always come together iv) vowels E and A never come togeth…

Let X be the random variable such that : P(X = –2) = P(X = –1), P(X = 2) = P(X = 1) and P(X > 0) = P(X < 0) = P(X = 0). Obtain the probability mass function of X and its distribution functions

A company study of product preferences of 10,000 consumers is as follows: products A. B and C were liked by 5015, 3464 and 4827 consumers, respectively. All the three products were liked by 500 consumers. Products A and B were liked b…

The lifetime of an electrical component normally distributed with mean 800 hrs and standard deviation of 60 hrs. What is the probability that the component will fail before 680hrs If standard deviation remain 60 hrs what would have …

Between z = 0 and z = 1.36

assuming that Huawei produces 5% of their total production of smartphones are defective. If 10 items are to be chosen at random from the production line, what then is the probability that; a. all smartphones are not defective? b…

How many scores are above 116?

The lifetime of a certain kind of bulb has a normal distribution with mean of 500 hours and standard deviation of 45 hours Find the percentage of bulbs with a lifetime of at least 570 hrs The percentage of bulbs with lifetime in bet…

Y10with usual OLS assumptions. Derive the expression for the error variance.

Making a sale on a customer call is 0.16 What’s the probability no sales will be made in 12 calls

Supposed three coins are tossed. Let X be the random variable representing the number of heads occur. Construct a table that shows the sample space and values of the random variable X.

Explain the following: • Probability Sampling and Non-Probability Sampling • Systematic sampling and Cluster Sampling • Advantages of Probability Sampling over Non-probability Sampling • Census vs. sample • Primary and Secondar…

A report says that 80% of India’s females aged 15-59 are not currently engaged in the workforce. A national agency has an opinion that this percentage may be even more. To validate its opinion, the agency did a survey of randoml…

What is regression analysis? Explain steps of performing regression analysis in detail? The following data shows the yearly sales (in million Rs.) of A2Zcorporation for the last nine years. Develop a regression model. Year 2011,…

Four balls are drawn in succession without replacement from an urn containing 4 white balls and 7 black balls. Let W be the random variable representing the number of white balls.

Use the given probability distribution table to answer each item. X 0 1 2 3 4 5 P(X) 0.10 0.24 0.08 0.20 0.21 0.17 1. P(2)= 2.P(greater than 0)= 3.P(less than 5)= 4.P(even)= 5.P(odd)= 6.P(between 0 and 5)= …

solve for the proportion of the area of the following probability notations then sketch the normal curve shading the required region of each given notation 1. P (-2 < z <1) 2. P (z > 3) 3. P (z < -2) 4. P (z > -1…

A committee of 5 members is to be formed from a group of 8 men and 5 women professionals. Let Y denote the number of women in the committee. If the selection is done randomly, determine the probability mass function of Y. What is the …

A population consists of the four numbers 1,2,8 and 9.List all the possible samples of size n=2 which can be drawn without replacement from the population.Find the following

. A population consists of the four numbers 1, 2, 8, and 9. List all the possible samples of size n = 2 which can be drawn without replacement from the population. Find the following: a. Population mean …

THE PROBABILITIES THAT A SURGEON OPERATES ON 3,4,5,6 or patients in any one day are 0.15,0.20,0.25,0.20 and 0.20 respectively

(a) The following table shows the number of units produced each month and the total incurred. MONTH UNITS COST JUNE 200 50,000 JULY 500 75,000 AUGUST 300 55,000 SEPTEMBER 800 95,000 OCTOBER 700 80,000 NOVERMBER 600 80,000 DECEM…

In a certain city, the daily consumption of electric power, X (in millions of kilowatt hours) is a random variable where X ~ Gamma (α, β) with a mean of 6 and a variance of 12. i) Find α and β. ii) Given a month has 30 days, how many …

supposed 100 refrigerator were manufactured during a day. ninety five operated perfectly and 5 had atleast one defect. a sample of four is selected at random. using the hypergeometric distribution formula, find the probability that 8 …

In an expirement where you roll a die and the random variable (X) is numbers that appears is even. What are the possible values of your random variable? 1 point

He wants to know how to identify the regions under the normal curve corresponding to different standard normal values. Your friend will send a picture of a normal curve with the corresponding area, and he asks you favor to explain eac…

Between z = 2.12 and z = -2.12

explain why the following experiments are not binomial. A. Rolling a die until a 6 appears. B. Asking 20 people how old they are. C. Drawing 5 cards from a deck for a poker hand.

Observe yourself in a day. find out how many Hours you spend in the following activities: House chores answering learning modules,Planting/Gardening, Using Social media,listening to music,watching television,and sleeping. Record your …

There are hundreds of apples on the trees, so you randomly choose just 45 apples and get a mean weight of 89.05 grams with a standard deviation of 4.43 grams. Assuming that the weight of the apples is normally distributed, what is the…

A new sneaker claims that it can make male athletes jump higher. A sample of 54 male athletes were asked to jump once with their own sneakers on and once wearing the new sneakers. The average jump increased by 0.98 inches with the new…

A random sample of 14 cigarettes of a certain brand has an average nicotine content of 3.7 milligrams and a standard deviation of 1.5 milligrams. What is the standard error of the 99% confidence interval for the average nicotine conte…

A random sample of 14 cigarettes of a certain brand has an average nicotine content of 4.4 milligrams and a standard deviation of 1.9 milligrams. What is the margin of error of the 99% confidence interval for the average nicotine cont…

A pair of fair dice is rolled. Let X the random variable representing the sum of the numbers that appear.Find P(3 ≤X≤ 10)

A box contains 4 yellow (Y) and 8 Pink balls. Six balls will be selected in the box. Determine the values of random variable P representing the number of pink balls.

3. The mean salary of ten employees is Php 32,000, and the median is Php 30,000. The highest-paid employee gets a Php 5,000 raise. a. What is the new mean salary of the ten employees? b. What is the new medi…

Four coins are tossed.Let T be the random variable representing the number of tails that occur.find the values of the random variable T

A random sample of 14 cigarettes of a certain brand has an average nicotine content of 3.8 milligrams and a standard deviation of 2 milligrams. What is the upper bound of the 99% confidence interval for the average nicotine content of…

Which of the following sampling method would be least likely to produce accurate and representative samples? a. Cluster Sampling b. Simple Random Sampling c. Systematic Sampling d. Snowball Sampling

A random sample of 14 cigarettes of a certain brand has an average nicotine content of 3.9 milligrams and a standard deviation of 2.5 milligrams. What is the lower bound of the 99% confidence interval for the average nicotine content …

Give at least 5 reasons why samples are used instead of population when conducting a research.

QUESTION ONE The manufacturer of product Gero requires three distinct processes A-C. On completion the product was passed from process C to finished goods stock. The following information was obtained in respect of the product 5,000…

The probability that an American industry will locate in Shanghai China is 0.70, in Beijing is 0.40 and in either Shanghai or Beijing or both is 0.80. what is the probability that the industry will locate : a) in both cities, b) in ne…

Calculate the width of the class with boundaries 5 and 30.

What is the probability or 4 out of 5 hands (dealer plus 4 players) receiving a "blackjack" (an Ace plus any 10 value card) all at the same time assuming all 104 cards are in play? Thank you

Find the probability of the following. A. P(z < 2.45) B. P(1.2

According to Dietary Goals for the US (1977), high sodium intake may be related to ulcers, stomach cancer, and migraine headaches. The human requirement for salt is less than 220 milligrams per day, which is surpassed in most single s…

a box contains five ball. the balls are numbered 1,2,3,4 and 5. a person randomly draws to balls from the box. let X be the sum of the numbers kf the ball drawn. what is the sum of all probabilities, P(X=x)?

Two balls are drawn in succession without replacement from a box containing 4 yellow balls and 3 white balls. Let Z be the random variable representing the number of white balls. Find the values of the random variable Z.

On the Standford-Binet test, the mean IQ is 100. A class of 21 kindergarten pupils were tested with a resulting mean of 100 and a standard deviation of 8.06. What is the standard error of the 90% confidence interval of the average IQ …

Make a study about how many sheets of paper you consumed weekly in answering your Self Learning Modules. Record the quantity (total number of sheets)per subject, then construct a probability distribution. Compute the mean, variance, …

In a group of students, the number of males and females studying Spanish, French or Music are given in a table below Spanish French Music Males 23 12 26 Females 12 15 09 i) Find the probability that a randomly c…

Supposed three coins are tossed. Let X be the random variable representing the number of heads occur. Construct a table that shows the sample space and values of the random variable X.

On the Standford-Binet test, the mean IQ is 100. A class of 21 kindergarten pupils were tested with a resulting mean of 99 and a standard deviation of 6.25. What is the margin of error of the 90% confidence interval of the average IQ …

1. Suppose five cell phones are tested at random. Let D represent the defective cell phone and let N represent the non- defective cell phone. If we let X be the random variable for the number of defective c…

Classify the following random variables as discrete or continuous the amount of calorie burned by the pasig athletes

Given the data 6, 9, 12, 15, 16, 19, 22. Construct a sampling distribution of the sample mean without replacement and repetition by selecting 2 samples at a time.

On the Standford-Binet test, the mean IQ is 100. A class of 21 kindergarten pupils were tested with a resulting mean of 108 and a standard deviation of 7.07. What is the upper bound of the 90% confidence interval of the average IQ of …

A coke float machine dispenses into 18-ounce cups. Test show that the actual amount of ice cream dispensed is normally distributed with a mean of 12.75 oz. and a standard deviation of 0.27 oz. a. what percent of cups will recei…

A dog gave birth of six puppies. Three of them are male while the rest are female. If you are to be given three puppies at random, list all the elements of the sample space using the letters M and F for male puppies and female puppi…

suppose a population consists of the numbers 2,3,5,8 and 12 what is the mean of the population?

On the Standford-Binet test, the mean IQ is 100. A class of 21 kindergarten pupils were tested with a resulting mean of 108 and a standard deviation of 7.09. What is the lower bound of the 90% confidence interval of the average IQ of …

4. [6] The table below gives 210Pb activities in a marine sediment core. Depth, L(cm) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 210Pb activity, AL(Bq kg-1) 247.0 199.0 160.0 123.0 101.0 78.0 62.0 46.0 38.0 Assume th…

the probabilities that a student gets 0, 1,2,3,4, or 5 mistakes are respectively. What is the average number of mistakes that a student makes in this class? What is expected value, variance and standard deviation of this discrete prob…

IN A SAMPLE OF OWLS IT IS FOUND THAT . There were 35 red males, 70 red females, 50 gray males, and 45 gray females IS THE COLOR INDEPENDANT OF SEX OF SAMPLE

A bag contains 3 black balls and 2 red balls,a ball is picked at random and replaced. what is the probability they are both black?

6. One of the following inferential analysis models is appropriate to test whether ‘There is a significant difference in students’ fear of SPSS before and after SPSS tutorial’. A. Independent samples t-test B. Paired samples…

Two coins are tossed and the random variable Z gives the number of heads. Find the range space, possible outcomes, and give the table of values.

the mean working hours of 400 college teachers was found to be 15.7 hours with standard deviation of 1.5 hours. test the hypothesis that the mean working hours is 16 hours against the hypothesis that it is greater than 16hrs at 1% lev…

the average hour spent using the computer by 20 senior high school students during online class is 7 hour with a standard deviation of 2 hours. construct a 98% confidence interval of average hour spent by all senior high school studen…

Solve the following problem: A government office has six telephone lines. For the past months, the probability distribution of the random variable Y which represents the number busy line per day in shown in the records below Y…

The number X of days in the summer months that a construction crew are cannot work because of the weather has the probability distribution X P(x) 6 0.03 7 0.08 8 0.15 9 0.20 10 0.19 11 0.16 12. 0.10 13 0.0…

7. An arithmetic test is given twice within a few days to a student. The highest possible score is 40. He receives a score of 35 the first time and a score of 18 the second time. If similarly varying results are obtained with other st…

In 2012 the Centers for Disease Control and Prevention reported that the rate of autism in children has risen to in 50. A study conducted in Norway suggests that the risk of autism may be significantly lower if women take folic acid s…

Suppose three test kits are tested at random. Let N be the random variable for the number of non - defective test kits, construct the probability distribution P(N). What can you conclude about the effectivity of the COVID-19 Rapid Ant…

Mrs. Paul wants to test that claim that, on average, her students' average mark is 85. She pulls the records of 100 per past student over a three-year period. The grades are inputted into MINITAB for analysis. Exhibit 1 below shows th…

a car salesperson as arrange a visit on three perspective customers in a week based on the past experiences helpers and laws that there is 10% chance of closing a sale on each visit determine the probability distribution of the number…

find the mean of the probability distribution of the random variable X and interpret its value, which can take only the values of 3,5, and 7, given that P (3) = ⁷/³⁰, P(5) = ⅓ and P(7) = ¹³/³⁰

Let the sample space be S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely. Compute the probability of the event E="an even number less than 7."

The probability that a tutor will see 0, 1, 2, 3, or 4 students x 0 1 2 3 4 P(x) 4/27 1/27 5/9 ? 5/27 (a) What is the probability that the tutor sees 3 students? (b) What i…

The number X of days in the summer months that a construction crew are cannot work because of the weather has the probability distribution X P(x) 6 0.03 7 0.08 8 0.15 9 0.20 10 0.19 11 0.16 12…

Jac tossed an unbiased coin. If the coin lands with head up on each toss, he wins ₱50. However, if it lands with tail up, he loses ₱60. If he continues to play the game, how much can he expect to win or lose in the game?

You are in a carnival and you see a game. The rule says that the outcome in the game is a random variable from 1 to 14 and that if the outcome is even, you win ₱50. If the outcome is odd, you win nothing. If you play the game, what …

Question 2 The probability that a house in an urban area will be burglarized is 5%. A sample of 50 houses is randomly selected to determine the number of houses that were burglarized. P (pass) = 0.05 q (failure) = 0.95 n = 50 (a) …

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