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?

Two cards are drawn from a deck. How many possible values can each of the following variables take? 1. sum of the numbers on the cards ___________ 2. number of times both cards are black ________ 3. Number of …

2. 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.…

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 S for the three tosses of the coin and to each sample point assign a value.

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.

1. The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 260 minutes and a standard deviation of 50 minutes. a. What is the probability that a battery lasts more…

1. Based from record, the mean weight of the newborn babies is 4.8 lbs with a standard deviation of 0.75 lbs. Out of 60 new born babies, find: a. The probability that the sample mean is less than 4.6 lbs b.The probability th…

1. Let X be random variable with values 4,5,6,7,8 and 9 a. Find the mean and the variance of the sample without replacement of n=2. b. Find a the sampling distribution of the mean and construct it's histogram 2. A…

A certain population has a mean of 15.4 and a standard deviation of 5.6. if random samples of size 5 is taken from this population, which of the following statements is true? * 1 point The standard deviation of the sampling distri…

A meeting of envoy was attended by 5 Koreans and 3 Filipinos. If four envoy were selected at random one after the other determine the values of the random variable K representing the number of Koreas.

1. Each main bearing cap in an engine contains 4 bolts. The bolts are selected at random without replacement from a parts bin that contains 30 bolts from one supplier and 70 bolts from another. a. b. What is the probability …

Observe yourself in a day. Find out how many hours you spend in the following activities: house chores, answering Self Learning Modules, planting/gardening, using social media like Facebook, messenger, tiktok, Instagram, and YouTube, …

Suppose the mean height of 200 students was 150 cm with a standard deviation of 12cm and mean weight was 60 kg with a standard deviation of 7kg

A firm employs 300 women and 100 men. The mean number of days absent last year for the women was 5.3 with a s.d. of 2.2 and for the men the corresponding figures were 6.2 and 2.9. Is the difference between the means significant at 5% …

How many possible samples of size n=8 can be drawn from a population of size 11

Permutation and Combination: In how many ways can 7 students be selected in a row of 7 seats if 2 of the students insist of sitting beside each other? In a gathering, the host make sure that each guest shakes hands with everyone else…

1. A coin is tossed twice. If the second throw results in tail a die is thrown. Describe the sample space for this experiment.

2. A random experiment has m outcomes a1,a2....,am and another has out out comes b1,b2.......,bn. Describe the sample space when both the experiment carried out.

3. A box contains 4 bad and 6 good tubes. Two are drawn out from the box at a time. One is tested and found to be good. What is the probability that the other one is also good?

How large a sample should be taken to be 95% sure that the error of estimation does not exceed 0.2 unit when standard deviation is 5?

How many people are likely to have a birthday that reads palindromically within their lifetime? (i.e.22/02/2022)

A laboratory supervisor in hospital is investigating number of reported on-the-job training accidents over a period of one month. Based on past records, she has derived the following probability distribution for x; where x is the numb…

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

Discrete or Continuoes sThe number of glasses in a dishwasher * 2 point Discret Continuouses The number of dropouts in a school per district The time taken to complete a puzzle The volume of water in a bottle

A Average Senior high school annual cost of tuition fee for all private schools last year was php 43.700. a random sample of cost this year for 45 private schools indicated that the sample mean was 45,800 and a sample standard deviati…

Two coin's are tossed. Let H be the number of Tails that occur. Determine the values of the random variable H.

In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at random will lie a. above score 50? b. below score 38? c. between 35 a…

Let Y be the random variable representing the number of tails that occur. Find the values of the random variable Y

A committee of 6 can be formed from a group of 5 sophomores, 7 juniors, and 8 senior. In how many ways can these be done if: A. there are 2 members from each class on the committees B. there shall be exactly 3 seniors, 2 jun…

70 years, and the standard deviation was 5.1 years. If a sample of 50 people from this region is selected, what is the probability that the mean life expectancy will be less than 71 years?

Number of times the first card is face card and the second card is not face card

A population consists of the five measurements 1, 3, 4, 6, and 8. Suppose samples of size 3 are drawn from this population. Construct a table, solve for the mean, variance and standard deviation.

When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 39 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3…

Suppose three coins are tossed. Let S be the random variable representing the number of heads that occur. Determine the sample space and the values of a random variable

As a fundraiser, the drama club decides to sell candy and cookies at noon hour. The club can purchase supplies from the cafeteria and may choose to buy from the following list if items:  five types of chocolate bars  four types …

In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at random will lie c. between 35 and 53?

Find the are to right of z=2.78

The numbers 5, 10, 15, and 20 are written on slips of paper, which are then placed in a hat. Two slips are randomly selected with replacement. Find the mean of the samples where the first is smaller than the second.

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…

(b) Patients arrive at a hospital accident and emergency department at random at a rate of 6 per hour. Find the probability that, during any 90 min. period, the number of patients arriving at the hospital accident and emergency …

When preparing a bouquet, a florist can choose from seven roses, six carnations, and four chrysanthemums. How many bouquets can the florist make if the bouquet must have at least one flower?

A stockroom clerk returns three safety helmets at random to three steel mill employees who had previous checked them. If Gary, Yuri and Cris, in that order, receive one of the three hats, list all the sample points for the possible or…

The probability density shown in Figure 5.21 is the exponential distribution f (x) = 0.55 e−0.55x 0 < x 0 elsewhere Find the probability that (a) the time to observe a particle is more than 200 microseconds; (b) the time to…

A change is made to one product page on the retail companies’ web site. To determine if the change does improve the efficiency of that product page, data must be collected on the proportion of visitors to the new page that ultimat…

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 me…

A fair spinner has 9 equal sections: 2 red, 3 blue and 4 green. It is spun twice. What is the probability of getting not green then green?

Suppose three cellphones are tested at random.let D represent the defective cell phone and N represent the non defective cellphone.if we let X be the random variable for the number of defective cellphones,construct the probability dis…

Two coins are tossed. Let H be the number of tails that occur.Determine the values of the random variable H.

A meeting of envoys was attended by 4 Koreans and 4 Filipinos. If three envoys were selected at random one after the other, determine the values of the random variable K representing the number of Koreans.

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. with the distribution of 0.75

If the probability density function of a random variable X is given by 𝑓(𝑥) = {2𝑘𝑥𝑒 − 𝑥2 , 𝑥 > 0 0, 𝑥 ≤ Determine (i)k (ii)distribution function.

If the two coins are tossed which is not a possible value of the random variable for the number of tails

The probabilities of machine manufacturing 0,1,2,3,4 and 5 defective parts in one day are 0.75,0.17,0.04,0.025,0.01 and 0.05 respectively. Find the mean of the probability Distribution

Four coin are tossed, let Z be the random variable representing the number of heads that turn up.find the value s of the random variable Z.

Four coins are tossed, Let H represent the head and T represent the tail. Let Y be the random variable representing the number of tails that occur. List all the possible outcomes and the corresponding values of the random variable Y

The ages of SHS students enrolled at ISNHS are normally distributed with a mean of 17 years and a standard deviation of 2.5 years. If a student is selected at random, what is the probability that his age is under 16 years?

A man has three routes from his home and he is equally likely in choosing these three ways.the chance that he will miss the train on choosing these three ways are respectively .25,.3,.35.one day he missed train find the probability th…

Find each of the following percentile points under the normal curve. Complete your procedures and find the corresponding z-score of each problem. Paragraph 2. Between z=-0.78 and z=-1.95 2. P32 1. P99

A reasearcher chose the participants of his study by selecting every 8th member of the population

The heights of Grade 11 male students in your school are normally distributed with a mean of 168 cm and standard deviation of 10 cm. Describe sampling distribution of 25 students wo are randomly drawn from the population.

The probabilities that a surgeon operates on 3, 4, 5, 6, or 7 patients in any one day are 0.15, 0.20, 0.25, 0.20 and 0.20, respectivel

Plasma glucose levels are used to determine the presence of diabetes. Suppose the mean ln (plasma-glucose) concentration (mg/dL) in 35- to 44-year-old is 4.86 with a standard of 0.33. A sample of 26 sedentary people in this age group …

In a box of switches, it is known that 10% of the switches are faulty. A technician is wiring 30 circuits, each of which needs one switch. What is the probability that (a) all 30 work (b) at most two of the switches do not w…

There are three Groups A,B and C with no. of persons 50, X, 90. The mean and Standard deviations for these groups are 113, Y, 115 and 6, 7, Z respectively. The Combind n , mean and Standard deviation for three groups are 200,116 and 7…

The following data is given Age (in years): Below 10, below20, below30, below40,below50, below60, below70, below 80 and No. of persons: 2,5,9,12,14,15,15.5,15.6 Find mean , median and mode.

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 …

2,4,5,6,7,8,9,10,12,14

fifty android tablet will be Delivered to a certain school for testing but five of them are defective.The principal will get two of these tablets for testing.Let X represent the defective tablet,Y for non defective tablet and Z repres…

A nationally known supermarket decided to promote its own brand of soft drinks on TV for two weeks. Before the ad campaign, the company randomly selected 40 of its stores across the United States to be part of a study to measure the c…

What is the probability that a market inspector will discover at least three violations of the public health code

If two coins are tossed, which is not a possible value of the random variable for the number of heads?

Four coins are tossed.Let A be the random variable representing the number of heads the occur.Find the value of the random variable A

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

Construct the probability histogram

a. List the sample space in the given experiment. How many outcomes possible? b. Construct a table showing the number of defective computers in each outcome and assign this number to this outcome. What is the value of the random v…

A technician has to choose three chips at random from 4 chips 2 of which are defective. Let's Z represent the number of non- defective chips chosen. What are the possible values of Z given that the first chip chosen is defective?

A survey showed that % of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If adults are randomly selected, find the probability that of them need correction for their eyesight.

A life insurance company will sell a 1 million three-year term life insurance policy exclusive in a particular risk group for a premium of ₱2,000.00. Let X denote the net gain to the company from the sale of one policy. If a person in…

The amount of coffee dispensed in a dispensing machine is normally distributed with a mean of 190 ml and a standard deviation of 10 ml. What is the z-value that will give an area of 0.975 on the right side of the normal curve?

I roll a fair die repeatedly until a number larger than 4 is observed. Let N be the total number of times until a number larger than 4 is observed. Find Pr(N=k) for k=1,2,3

How many samples of size n=3 can be drawn from this population?

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.

A 2-hour movie runs continuously at a local theater. You leave for the theater without first c checkingthe show times. Use an appropriate uniform density function to find the probability that you will arrive at the theater within 10 m…

The proportion of assignments completed within a given day is described by the probability density function f (x) = 12(x - x^3 ) for 0 ≤ x ≤ 1. Find the expected proportion of completed assignments [4 marks].

The proportion of assignments completed within a given day is described by the probability density function f (x) = 12(x - x3) for 0 ≤ x ≤ 1. Find the expected proportion of completed assignments.

Probability value is a number from −1 to 1

1.List the sample space 2.count the number of tails in each outcome and assign this number to this outcomes. 3.construct the frequency distribution of the values of the given random variable. 4.construct the probability distributio…

A secretary commits 0,1,2,3,4, or 5 encoding errors on a given hour with probabilities 0.09, 0.30, 0.25, 0.15, 0.10, and 0.06 respectively. Find the probability that on the next hour she will commit more than 5 errors.

A Population Has A Mean Of 73.5 And A Standard Deviation Of 2.5

An umbrella check girl returns 2 umbrellas at random to 2 customers who had previuosly checked in namely andrea and althea. If Andrea's umbrella was black and althea's umbrella was yellow. List the elements of the samplke space all po…

A Population Has A Mean Of 73.5 And A Standard Deviation Of 2.5 A. Find the mean and standard deviation of x for samples of size 30 B. Find the probability that the mean of a sample of size 30 will be less than 72

The probabilities that a bias die will fall as 1, 2, 3, 4, 5, or 6 are ½, 1/6, 1/12, 1/12, 1/12, and 1/12, respectively.

Let us suppose that the body weights of 800 students have a normal distribution with mean l = 66 kg and standard deviation r = 5 kg. Find the number of students whose weight is: a) between 65 and 75 kg; b) over 72 kg

Four balls are drawn in succession without replacement from an urn containing 4 red balls, 3 blue balls and 3 yellow balls. Let Z be the random variable representing the number of blue balls.

Identify possible samples for the following populations: 1. Students enrolled in schools along university belt 2. Athletes participating in the 2005 summer Olympics 3. Electric consumption of families in the national capital …

A meeting of consuls was attended by 4 Chinese and 2 Japanese. If three consuls where selected at random one after the other, determine the values of the random variable J representing the number of Japanese.

The number of patients seen in the Emergency Room in any given hour is a random variable represented by x. The probability distribution for x is : X 10 11 12 13 14 P(X) 0.4 …

A manufacturing firm produces steel pipes in three plants with daily production volumes of 500, 1000 and 2000 units respectively. According to past experience, it is known that the fraction of defectives output produced by the three…

5. What is the probability that a market inspector will discover, greater than five violations of the public health code?

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