Solved: An inventor has developed a new, energy efficient lawn mower engine. He claims that the engine will run continuously for 5 hours (300 minutes) on a single gallon of regular gasoline. Suppose a simple random sample of 50 engines is tested. The engines run for an average of 295 minutes, with a standard deviation of 20 minutes. Test the hypothesis that the mean run time is 300minutes against the alternative hypothesis that the mean run time is not 300minutes using a 0.05 level of significance

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 and the…

X=82

Two balls are drawn in succession without replacement from an urn containing 4 red balls and 5 blue balls. Let R be the random variable representing the number of red balls. Find the values of the random variable R.

Random samples with size 4 are drawn from the population containing the values 14, 19, 26, 31, 48, and 53 a. Construct a sampling distribution of the sample means. b. Find the mean of the sample means. c. Compute the …

julia and tony play and game rock paper scissor assume that at each play they make their choices with equal probability 1/3 for each of the three moves and dependently of any previous play A.)on any single play,what is …

Find the probability distribution of a random variable X representing the outcome when a single die is rolled once. 2 Three cards are drawn in succession from a deck without replacement. Find the probability distribution for th…

Four coins are tossed. Let Z be the random variable representing the number of tails.

Supposed to laptops or tested . If we let x be the random variable representing the number of defective laptops . What are the possible values of the random variable ?

A basket contains 10 red balls and 4 white balls.If three balls are taken from the basket one after the other,determine the possible values of the random variable R representing the number of red balls.

In a box are 2-balls one white and one yellow. Two balls are picked one at a time with replacement. Let X be the random variable representing the number of white balls.

Three balls are drawn in succession without replacement from an urn containing 3 red balls, 2 blue balls and 2 yellow balls. Let Z be the random variable representing the number of blue balls. Sample space (all outcomes) P…

In a betting game wherein the result may be one of the following in one turn: break even, win 5 peso or lose 3 peso. How much will be the amount a player gets after three turns. Let X be the total amount of a player gets after three t…

A shipment of five computers contains two that are slightly defective. if a retailer receives three of these computers at random, list the elements of the sample paces using the letters D and N for defective and non-defective computer…

what is the factor given that the size of the population is 500 and samples of size 50 are drawn from this population

Complete the table below. Experiment 1. Number of rings before the phone is answered 2. Teacher ask the students to finish the test after an hour 3. Number of complaints per day 4. Height of the tallest building in Lucena City 5…

A basket contains 8 ripe and 6 unripe bananas. If three bananas are taken from the basket one after the other. Construct a table that shows all the possible outcomes of the random experiment and all the values of the random variable R…

Two balls are drawn in succession without replacement from a box containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Find the values of the random variable Z.

In a challenging chess game, the probability that Mr.B will win is 0.67. Assume that the chess competition follows a binomial distribution and 7 separate matches will be played. Determine: (a) will win at most 3 matches (b) wi…

Let T be a random variable giving the number of heads plus the number of tails in three tosses of a coin. List the elements of the sample space for the three tosses of the coin and assign a value to each sample point.

Suppose three coins are toosed let y be the random variables representing the number of heads that occur. A. Find the values of the random variables Y. Complete the table below.

A pair of fair dice is rolled. Let X 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. Find P(X≤ 7) D. Find t…

Given W is a uniformly distributed random variable with mean 33 and variance 3. determine: (a) probability density function for W (b) cumulative distribution function for W

A.classify the following random variables as discrete or continuous. 1.The weight of the professional wrestlers

Given the μ=65 and σ=5 of a population of Math Exam scores. The z−value that corresponds to a score of X=74 is

As studied, the average number of hours spent by senior high school students for their online classes a week is 25 hours with a standard deviation of 4 hours. Assuming that study is true and the data is normally distributed. Find t…

Two balls are drawn in succession without replacement from a box containing 3 red balls and 4 yellow balls. Find the possible outcomes and the values X of the random variable X, where X is the number of yellow balls. Use R for red bal…

Given the data: 123, 126, 129, 132, and (a) construct a sampling of the mean (b) draw a histgyfor the sample means

Permutation: 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? …

As studied, the average number of hours spent by senior high school students for their online classes a week is 25 hours with a standard deviation of 4 hours. Assuming that study is true and the data is normally distributed. Find t…

Mrs. Balao is randomly choosing 3 students for a team who will compete in a math quiz bee, and there are 5 girls and 8 boys to choose from. What is the probability of having a team made up 2 girls and a boy?

An experiment consists of asking three Grade 10 students at random if they prefer to choose the Academic track or TVL track in the senior high school. Use A for Academic and T for TVL. Let Y represent the random variable representing …

A study was conducted to determine the average salary of a teacher. With this, 81 teachers were invited as samples. It was known that the mean salary of these sample teachers is Php 24,000.00 with a standard deviation of Php 1,000.00.…

An experiment consists of asking three Grade 10 students at random if they prefer to choose the Academic track or TVL track in the senior high school. Use A for Academic and T for TVL. Let Y represent the random variable representing …

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 …

How many children have heights between 98 cm and 104 cm?

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 41 male athletes were asked to jump once with their own sneakers on and once wearing the new sneakers. The average jump increased by 1.28 inches with the new…

How many children belong to the upper 15% of the group?

suppose 100 refrigerator were manufactured during a day. ninety five operated perfectly and 5 had at least one defect. a sample of four is selected at random

Mr. Ybarola conducted an examination on his subject. He has determined that the mean score of all those who had taken the test is 89 and its standard deviation is 4. 1. Determine the 𝑧-score of Karlie who scored 94 in th…

A group of people were asked if they had run a red light in the last year. 302 responded “yes”, and 158 responded “no” find the probability that if a person is chosen at random, they have run a red light in the past year.

A shipment of five computer contains two that are slightly defective. If a retailer receive three of computers at random,list the elements of the sample paces using the letters D and N for defective and non-defective computers, respec…

a new brand of handbags comes in 5 different designs and each available in 4 different colors. If an outlet wishes to display these handbags with all the design and colors, how many handbags should be displayed

From a box containing 4 black balls and 2 green balls,3 balls are dawn in succession. Each ball is placed back in the box before the next draw is made. Let G be a random variable representing the number of green balls that occur. Find…

Mean height of 100 Students is 150 cms and the standard deviation is 15 cms. Assuming that the height are normally distributed, find how many students have height between 110 to 165 cms.

in a random sample of 120 teachers 48 of them have master's degree. find the value of p

Given W is a uniformly distributed random variable with mean 33 and variance 3. Using R programming, apply the suitable coding to identify answer in (a) and (b) (a) probability density function for W (b) cumulative distribution …

in a random sample of 120 teachers, 48 of them have master's degree find the value o p

1. A questionnaire asks shareholders of a company to state whether they consider the chairman’s salary to be too high, about right, or too low. Excluding shareholders who have no opinion, the probabilities of answers from randomly sel…

a meeting of consuls was attended by 4 Americans and 4 Germans. If three consuls were selected at random, construct the probability distribution of the random variable G representing the number of Germans.

a sample of 150 students were chosen at random from grade 11 students who have laptops.Pampanga. the sample indicated that 75% of them were in favor of having an educational trip. find a) 95% and b) 99% confidence intervals for the pr…

A shipments of five computers contains that are slightly defective. If a retailer receives three of these computers at random list the elements of the sample space 5 using the letters D and N for defective and non-defective computers …

A family has four children. If Y is random variable that pertains to the number of female children what are the possible values of Y?

Suppose a population is composed of only 3 measures: 1, 2, and 3. The possible samples of size 2 can be draw from this population. List all the possible sample size 2 when repetition allowed or with replacement.

Two cards are drawn from a deck. How many possible values can each of the following variables take? 5.) Number of times the first card is face card and the second card is not a face card

A certified public accountant (cpa) randomly selects 4 accounts for a group of 12 careful examination. The company being audited knows that 7 of the accounts contain - errors. what is the probability that all 3 accounts selected are e…

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.

Lending institutions normally publish their base lending rates in the print media. However, the actual lending rates vary from one lender to another. To estimate the mean lending rate, a financial a advisor takes a random sample of ni…

Let X be a ramdom variable with the following probability distribution x: 1, 2, 3, 4 P(X=x): 0.4, 0.3, 0.2, 0.1 a. Find E(X) and Var(X) b. is E(X) a possible value of X

Random sample of 400 men and 200 women is locality were whether they would like to have bus stop near their residence 200 men and 40 women are favor of proposal the test is there any significance diff b/w men and women at 5%.

An investigator thinks that people under the age of forty have vocabularies that are different than those of people over sixty years of age. The investigator administers a vocabulary test to a group of 31 younger subjects and to a g…

the result of a particular examination are given in the table below passed with distinction 10% passed without distinction 60% failed 30% it is known that a candidate fails in the examination if he obtains less than 40 marks while…

give me the answer of variance and standard deviation of P(3)=7/30 P(5)=1/3 and P(7)=13/30 by following the steps

Illustrate the probability distribution if X is the random variable that represent the number of recoveries

Fuel consumption tests are conducted for a particular model of car. If a 95% confidence interval with a margin of error of 0.6 kilometer per liter is desired, how many cars should be used in the test? Assume that a preliminary test in…

An inventor has developed a new, energy efficient lawn mower engine. He claims that the engine will run continuously for 5 hours (300 minutes) on a single gallon of regular gasoline. Suppose a simple random sample of 50 engines is tes…

You are thinking of using some leftover ceramic tiles to make a decorative border for a patio. You have ten blue, four gold, and six white tiles. In how many ways can you place the tiles to make the border if you need 12 tiles and y…

At Statsville High School, 125 students are taking university-preparation Science courses. Of these students, 64 take Biology, 40 take Chemistry, and 51 take Physics. There are 12 students who take both Chemistry and Physics, 11 who t…

There are 18 pieces of music to choose from: 6 for piano, 5 for violin, and 7 for guitar. In how many ways can you choose 3 pieces of music, if at least 1 must be for piano? Explain your reasoning. (3 marks)

In a National Achievement Test, suppose three test booklets are tested at random. Let D represent the defective test booklet and let N represent the non-defective test booklet. Let X be the random variable representing the number of n…

A meeting of consuls was attended by 4 Americans and 2 Germans. If three consuls were selected at random, construct the probability distribution of the random variable G representing the number of Germans

In a certain Algebra 2 class of 30 students, 7 of them play basketball and 15 of them play baseball. There are 10 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball …

How can I draw a normal curve with a mean of 60 and a standard deviation 12?

1. A recent study reported that an estimated 70% of professionals in IT have considered moving to U.S to earn a higher salary. The report further stated that this estimate is considered accurate within three percentage points, and c…

A random sample of size 4 is taken with replacement from a population with mean 12 and variance 8.Determine the mean ,variance,and standard deviation.

Gillbert got a new job in a shoe store. The number of pairs of shoes he was able to sell for three days are 2, 4, and 5. Assume that samples of size 2 are randomly selected with replacement from this population of three values. a. Li…

The results of the nationwide aptitude test in mathematics are normally distributed with mean=63 and standard deviation =5 . What is the 97.5th percentile?

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…

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