Solved: 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 labour hours before and after the industrial safety awareness program is (2.282, 8.118) in hours. Interpret the confidence interval. A 90% confidence interval for the average salary (in RM) of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was (139,048, 154,144). Give a practical interpretation of the interval.

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?

A company manufactures fuses. The percentage of non-defective fuses is 95.4%. A sample of 10 fuse was selected. Calculate the probability of selecting at least 3 defective fuses.

Two balls are picked in succesion without replacement -4 white balls and 5 green balls. Let Y be the random variable representing the number of green balls

According to USA Today (March 18, 1997), of 4 million workers in the general workforce, 5.8% tested positive for drugs. Of those testing positive, 22.5% were cocaine users and 54.4% marijuana users. (a) What is the probability that of…

Four coins are tossed.Let Z be the random variable representing the number of heads that occur.Find the values of the random variable Z

Suppose that each firm currently catches $100 worth of fish per year, and there is $200 worth of fish left in the lake. In the following spreadsheet, enter the amount that each firm would earn in each of the next 10 years if the two f…

A company manufactures soaps. The mean mass of the soaps is 300g with variance 52g. A sample of 100soaps was selected. a)Find the probability of selecting soaps more than masses 320g. b)How many soaps will have masses between 280g a…

Explain the following concepts using examples: i. Mutually exclusive events. (3 Marks) ii. Independent events. (3 Marks)

The Star hotel was burned down in a fire and the manager decided to accommodate the guests in 4–person and 8-person tents. The tents were to be hired at a cost of Kshs 1,500 and Kshs 4,500 per night respectively, the space available c…

Suppose that a pair of fair dice are to be tossed and let x the random variable denote the sum of the points. compute the expected value the variance of X the standard deviation of x

A company manufactures soaps. The mean mass of the soaps is 300g with variance 52g. A sample of 100soaps was selected. a)Find the probability of selecting soaps more than masses 320g. b)How many soaps will have masses between 280g a…

Suppose an average of 5 cars arrive at the parking lot every 15 minutes. What is the probability that exactly 4 cars will arrive in the next 15 minutes?

Given the score X=72, σ=4 and z=1.64, the value of μ is

If the x̄ =87 and the s=7, the z−score that corresponds to a score X=102 is

The area between z = -2.40 and z = 1.15 is

Four coins are tossed. Let Z be the random variable representing the number heads that occur. Find the values of the random variable Z. ( Take note that you should have 2 = 16 possible outcomes ).

A coin is tossed, and the random variable X is the number of heads that appear. Use H to represent the head and T to represent the tai

After several months of planting roses, Siti measures the height in centimeters each of the plant. The height of the plants is given as below: 38, 14, 22, 36, 35, 29,19, 24, 32, 35, 41, 47 a) Construct a stem-and-leaf diagram…

An analysis of the monthly allowances received by a sample of five engineers from a telco company has been conducted recently. The mean and median of the allowances is RM7000. A unimodal among the observations is RM12,000. Fi…

a) Let the mean concentration of particulate matter collected on filter paper is 45.6 ppm, with the standard deviation is 4.4 ppm. Find the probability that the mean concentration of particulate matter in a sample of 87 filter papers …

Independent Assessment 2 Four coins are toss. Let Y be the random variable representing the number of tails that occur. Find the values of the random variable Y. Possible Outcomes Value of Random Variable Y (number of tails)

An analysis of the monthly allowances received by a sample of five engineers from a telco company has been conducted recently. The mean and median of the allowances is RM7000. A unimodal among the observations is RM12,000. Find the st…

Let the mean concentration of particulate matter collected on filter paper is 45.6 ppm, with the standard deviation is 4.4 ppm. Find the probability that the mean concentration of particulate matter in a sample of 87 filter papers w…

DIRECTION: Find the mean, variance, and standard deviation of the discrete random variable X with the following probability distribution.(5 points each) 1. X P(X) 0 0.2 1 0.3 2 0.2 3 0.2 4 0.1 2…

A coin tossed and a die is rolled. The outcome of the coin is recorded 1 when it show a head and 0 when it shows a tail. The random variable R gives the sum of the outcomes of the coin and the die. Compute the average value of the ran…

A population consists of six scores: 11,13,15,16,17 and 19. If a sampling distribution of size 3 is drawn from the population. Compute for the population of mean, variance, variance of the sampling distributions of the sample mean and…

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 …

An analysis of the monthly allowances received by a sample of five engineers from a telco company has been conducted recently. The mean and median of the allowances is RM7000. A unimodal among the observations is RM12,000. Find the st…

A lottery that pays off P300 000 000 is made available for 10 000 000 tickets. Each ticket costs P50. Suppose the variable Z gives the net winnings from playing the lottery. What is the expected gain for joining the lottery with only …

A random sample of n= 21 items is taken, resulting in a sample mean x¯= 17.0 with a sample standard deviation of s= 4.9. Assume x is normally distributed and use this information and α 0.05 test the following hypotheses. H0: μ = 16 …

Bag I contain 3 red and 4 black balls and Bag II contain 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red. Find the probability that the t…

The proportion of eligible voters in the next corporation election (in tumkur) who will vote for the incumbent is assumed to be 55%. What is the probability that in a random sample of 500 voters less than 49% say they will vote for th…

A group of students got the following scores in a test:6,9,12,15,18 and 21. Consider samples of size 3thag can be drawn from this population. List all the possible samples and the corresponding mean.

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