Solved: A wallet contains a Php 20-bill, a Php 50-bill, and a Php 100-bill. A bill is taken out from the wallet and then replaced with a bill of the same amount that was taken away. If a bill is taken out from the wallet, what is the probability that the sum of the bill is more than Php 40?

The manufacturer of the Horizon truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. Assume the mileage wear follows the normal distribution and the standard deviation of the distr…

A labor union claims “40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job were available” 74 persons out of the 200 sampled said they would return to work. Can we conclud…

There are two octahedral dice with faces marked 1 through 8. They are constructed such that the side 8 is 1.5 times as probable as the 2 through 7 and the sum of the probabilities of the 1 and the 8 equals that of the pairs on opposin…

Suppose two dice was rolled. Let Y be the random variable representing the number of even number that occur. Find the values of the random variable Y.

For each of the following scenarios, give an example of a discrete and a continuous random variable. The first one is done as an example. Scenarios •Asking your classmates about their breakfast. •Making an order at a fast food r…

Among 250 employees, of the local office of an international insurance company, 182 are whites, 51 are blacks and the rest are Orientals. If 5% margin of error is used, 5. How many employees will be chosen for a case study as sample…

Given \mu=118, \sigma=29μ=118,σ=29 then, p(76\lt x\lt 144)=p({76-118\over29}\lt Z\lt{144-118\over29})=p(-1.45\lt Z\lt 0.90)p(76

A population is normally distributed with a population mean of 76 and a population standard deviation of 13. i. State the distribution of the sample mean for simple random samples of size n = 100. ii. Given a simple random sample …

Given a standard normal distribution with mean =78 and standard deviation = 28, find P(85 < X < 102)

Given a standard normal distribution with mean =118 and standard deviation = 29, find P(76 < X < 144)

Given a standard normal distribution with mean =136 and standard deviation = 39, find P(X>84)

Suppose a particle moves along the x-axis beginning at 0. It moves one integer step to the left or right with equal probability. What is the probability function of its position after four steps?

Suppose a fair die is tossed two times. Let X be the larger of the two faces that appear. Find px(k).

Given a standard normal distribution with mean =62 and standard deviation = 44, find P(X>92)

Given a standard normal distribution with mean =58 and standard deviation = 40, find P(X<96)

A man has four keys in his pocket and, since it is dark, cannot see which is his door key. He will try each key in turn until he finds the right one. Let X be the number of keys tried (including the right one) to open the door. Wha…

Given a standard normal distribution with mean =60 and standard deviation = 35, find P(X<75)

An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 814 hours and a standard deviation of 42 hours. Find the probability that a bulb burns between 747 and 846 hours.

A class in statistics contains 10 students, 3 of whom are 19, 4 are 20, 1 is 21, 1 is 24, and 1 is 26. Let X be the average age of the 2 randomly selected students and derive the probability function for X.

An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 799 hours and a standard deviation of 49 hours. Find the probability that a bulb burns between 769 and 878 hours.

The weights of 1,000 children, in average, is 50kg with standard deviation of 14kg. Suppose the weights are normally distributed, how many children weigh between 53kg and 68kg?

The weights of 1,000 children, in average, is 46kg with standard deviation of 20kg. Suppose the weights are normally distributed, how many children weigh less than 63kg?

The weights of 1,000 children, in average, is 55kg with standard deviation of 17kg. Suppose the weights are normally distributed, how many children weigh greater than 38kg?

A random sample of size 144 is drawn from a population whose distribution, mean, and standard deviation are all unknown. The summary statistics are x−−=58.2 and s = 2.6.

Let XX be a random variable represented by the sum of the outcomes, There are 4^2=164 2 =16 possible outcomes with replacement 2: (1, 1)2:(1,1) 3: (1, 2), (2, 1)3:(1,2),(2,1) 4: (1, 3), (2, 2), (3, 1)4:(1,3),(2,2),(3,1) 5: (1, 4…

A box contains 5 balls. One is numbered 1, three are numbered 2, and one is numbered 3. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is rep…

•Box A and B contains 1, 2, 3, 4. Construct the probability distribution and draw a histogram of the sum when one number from each box is taken with placement

How many ways 6 delegates to the convention from a group of 24 qualified students

Random samples of size n were selected from binomial populations with population parameters p given here. Find the mean and the standard deviation of the sampling distribution of the sample proportion ^p = X \bar in each case: …

In how many ways can a teacher select 6 delegates to a national convention from a group of 24 students

The scores for a mathematics course seem to be normally distributed with mean 70 & standard deviation of 8. If the instructor wishes to give an A grade to 10% of the students, what should be the dividing line between an A grade and a …

suppose the weight of 800 students are normally distributed with mean 75kg and standard deviation 5kg. find the numer of students that weigh more than 80kg

Suppose that the bank customers arrive randomly and independently on an average of 3.2 customers every 4 minutes. What is the probability that: a. Exactly two customers arrive in every 4 minutes? b. Exactly two customers will arriv…

Oranges chosen at random have a mean mass of 210 grams and standard deviation of 35 grams. Assuming a normal distribution, what is the probability of choosing an orange with a mass between 170 grams and 250 grams

To compare the results of boys and girls in a class, a special test was given to 50 boys who averaged 67.4 with Sd. of 5.0, and 50 girls averaged 62.8 with Sd. of 4.6. (Group Assignment) (2 pts.) a) Test, at …

To compare the results of boys and girls in a class, a special test was given to 50 boys who averaged 67.4 with Sd. of 5.0, and 50 girls averaged 62.8 with Sd. of 4.6. (Group Assignment) (2 pts.) a) Test, at   0.05 …

A manufacturer of paper used for packaging requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour's production…

Let X be a binomial(5, 0.2) random variable. Let Y be a discrete random variable that is independent of X, such that Y = 1 with probability 0.2 and Y = 0 with probability 0.8. What is the probability that the sum of X and Y is less th…

A dataset has a mean of 15 km and a standard deviation of 2 km with n equal to 30. There is a mode of 22 km and a median of 18 km with a range of 20 km. What is the variance?

According to a hospital administrator, historical records over the past 10 years have shown that 20 percent of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospita…

Four coins are tossed let z e the random variable representing the number of heads that turn up. find the values of the random variable Z

Supposed five coins are tossed.let x be the random variable representing the number of head occur. Find the probability of each values of the random variable.

In a railway yard goods trains arrive that at the rate of 30 trains per day. Assuming that the inter-arrival time follows an exponential distribution and the service time distribution is also exponential with an average of 36 mi…

Using the sample in a family of four children, construct a probability distribution for the variable Z representing the number of boys. Draw the histogram of the probability distribution.

Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 oranges, with replacement being made after each drawing. Find the probability that (I) Both are white

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 the red balls

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

A student has to take 7 more courses before she can graduate. If none of the courses are prerequisites to others, how many groups of three courses can she select for the next semester?

An expirement study was conducted by a researcher to determine if a new time slot has an effect on the performance of pupils in Mathematics. Forty randomly selected learners participated in the study. Toward the end of the i…

A manufacturer of bicycle tires has developed a new design which he claims has an average lifespan of 15 years with standard deviation of 2 years. A dealer of the product claims that the average lifespan of 150 samples of th…

In a family with two children, find the mean of the number of children who will be girls

The lifetime of a light bulb is normally distributed with mean 800 hours and standard deviation 50 hours. A random light bulb is selected. What is the probability that it will last for more than 950 hours?

Suppose the IQ of the learners in a certain University follows a normal distribution with mean 110 and standard deviation 100? a What proportion of the learners population have IQ's more than 90 but less than 100? b. A random male …

The ages of participants in a drama workshop are normally distributed with mean 18.5 years and standard deviation 2.5 years. What is the probability that the age of a random participant is (a) more than 20 years, (b) between 16 and 18…

On the average, six people per hour use a self services banking facility during the prime shopping hours in a department store. Assuming the arrival of customers is random and independent; What is the probability that fewer than 5 peo…

In 2018, the braking distance of Toyota Camry cars on a wet surface follows a normal distribution. Its mean is 122 feet with a standard deviation of 20 feet. What is the probability that a randomly selected Toyota Camry will have a br…

On the average, six people per hour use a self services banking fasility during the prime shopping hours in a department store. Assuming the arrival of customers is random and independent; What is the probability that; One person will…

Students pass a test if they score 50% or more. The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively. Assuming this data is normally distributed, what perc…

The standard score of Mary in Chinese Test is 1.2 and her standard score in English Test is 0.8. In what subject did she perform better?

Students pass a test if they score 50% or more. The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively. Assuming this data is normally distributed, what perc…

1. The average weekly loss of labour hours due to factory accidents is studied on ten labours before and after a new industrial safety awareness program. The 95% confidence interval for the difference in mean of the weekly loss of lab…

A bakeshop owner determines the number of boxes of pandesal that are delivered each day. Find the mean of the probability distribution shown.

Type of random varial of number of black cards from an ordinary deck of cards

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

According to a study by the Pew Research Center, 15% of adults in the US do not use the Internet. Suppose 10 adults in US are selected randomly. a. Is the selection of the 10 adults a binomial experiment? b. What is the pr…

find class boundaries, midpoint, and width for the class 18.8 - 22.6

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 mean of the probability distribution of the random variable X, which can take only the values 2,3,4,5 given that p(2)= 2/7, P(3)= 3/7, P(4) = 1/7, and P(5)= 1/7.

For each of the following scenarios, give an example of a discrete and a continuous random variable. The first one is done as an example. Scenarios •Asking your classmates about their breakfast. •M…

Let X be a discrete random variable such that X = 0 with probability 0.5 and X = 1 with probability 0.5. Let Y be a discrete random variable such that Y = 0 when X = 1 and Y = 1 when X = 0. What is the mean and variance of X + Y?

A box contains 5 green and 2 blue dice.Four dice are chosen one after the other .Determine the values of the random variable G representing the number of green dice.

4. A soft-drink machine is regulated so that it discharges an average of 200 mls per cup. If the amount of drink is normally distributed with a standard deviation equal to 15 mls. Below what value do we get the smallest 30% of the cup…

a taxi cab company has 12 ambassadors and 8 fiats. If 5 of these taxi cabs are in workshop for repair, calculate the probability that i) 3 of them are ambassadors and 2 flats ii) all the 5 are of the same make

1 4 4 2 3 4 5 1 4 1 Work out the mode

A spinner for a child's game has the numbers 1 through 9 evenly spaced. If a child spins, find each probability: a. The number is divisible by 3.

Suppose that the four inspectors at a film factory are supposed to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in ev…

Regression of yi = ꞵ0 + ꞵ1 xi1 + ꞵ2 xi2 + ꞵ3 xi3 + ꞵ4 xi4 + ui yields the following results in tabular form. The tabulated t- statistics is 2.6 , 1.96 and 1.64 for one , five and ten percent significance levels respectively. State the…

A spinner for a child's game has the numbers 1 through 9 evenly spaced. If a child spins, find each probability: a. The number is divisible by 3. b. the number is greater than 7. c. The number is an even number.

a) Consider the following functional relation, f, defined as: f : R \rightarrow R, f(x) = x2 Determine whether or not f is a bijection. If it is, prove it. If it is not, show why it is not. b) Consider the set F = {y | y = a…

Consider the lot of fluorescent tubes in number 100.if 50 samples of 100 tubes are drawn from the lot with replacement find the expected number of sample will have mean life atleast 1600 hrs. Flourescent tubes are 1570 hrs with a s.d.…

A recent survey found that 54.7% of the population own their homes. In a random sample of 150 heads of households, 92 responded that they owned their homes. At 0.01 level of significance does that indicate a difference from the nation…

Researcher is using data for a sample of 10 observations to estimate the relation between consumption expenditure and income. Preliminary analysis of the sample data produces the following data. ∑xy = 700 , 1000 2 ∑x = , ∑X = 1…

A report stated that the average age of commercial jets in country X is 14 years. An executive of a large airline company selects a sample of 36 planes and finds that the average age of the plane is 11.8 years. The standard deviation …

The odds of Matthew doing his math homework is 13:7. What is the probability of Matthew doing his homework once in the next two days?

Using the data given below, calculate the 3 and 5 years moving averages. Year 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 Sales 2354 2380 2319 2469 …

let x be a random variable with probability density function given by f(x)=(2he^-1/4x ; 0

A politician believes that 25% of all macroeconomists in senior positions would strongly support a proposal he wishes to advance. Suppose that this belief is correct and that five senior macroeconomists are approached at random. What …

FIND THE VALUES FOR EACH OF THE FF. CASES: A. UPPER TAIL AREA OF 0.025 WITH DEGREE OF FREEDOM=28 B. LOWER TAIL AREA OF 0.01WITH DEGREE OF FREEDOM=15 C. WHERE 90% OF THE AREA FALLS BETWEEN THESE TWO t-VALUES WITH df=9

the number of defective production in a production process follows a poisson distribution with a mean of 2.6 per month, for a given month what is the probability there will be fewer than two defective production?

According to the article "Are Babies Normal?" by Traci Clemons and Marcello Pagano published in The American Statistician, Vol. 53, No. 4, pp. 298-302, the birth weights of babies are normally distributed with a mean of 3388…

The owner of a factory that sells a particular bottled fruit juice claims that the average capacity of their product is 250 ml. To test the claim, a consumer group gets a sample of 100 such bottles, calculates the capacity of each bot…

According to the article "A Critical Appraisal of 98.6 Degrees F, the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich" published in the Journal of the American Medical Associ…

A factory manufacturing light-emitting diode (LED) bulbs claims that their light bulb last for 50 000 hours on the average. To confirm its this claim is valid, a quality control manager got a sample of 50 LED bulbs and obtained a life…

A box contains 18 light bulbs. Of these, four are defective. Five bulbs are chosen at random. What is the probability that four are defectives?

what happens to the variance of the sampling distribution of the sample means when the sample size increases

Determine if the following are probability distributions (if no, state why) x= {3,6,9,12,15} p(x)= {4/9,2/9,1/9,1/9,1/9}

The following represent the scores of a group of students on two tests. calculate spearman rs and kendall's tau for these data. Test 1 - 36, 34, 33, 29, 29, 28, 28, 28, 24, 22, 19, 12 Test 2 - 18, 26, 24, 18, 15, 12, 14, 13, 12, 10,…

1. To the left of z= -1.66 2.to the left of z=1.47 3.to the right of z=2.52 4.to the right of z= -1.75 5.between z=1.5 and 2.76

A wallet contains a Php 20-bill, a Php 50-bill, and a Php 100-bill. A bill is taken out from the wallet and then replaced with a bill of the same amount that was taken away. If a bill is taken out from the wallet, what is the probability that the sum of the bill is more than Php 40?

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