Solved: An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 808 hours and a standard deviation of 93 hours. Find the probability that a random samples of 19 bulbs will have an average life of greater than 799 hours.

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.

A population consist of the values 2,4,6 and 8 a) List all the possible sample size 2 when drawing with replacement and compute the mean of each sample. b)Construct the sampling distribution of the mean. c) Compute the mean, varian…

Q−5: a) An urn contains 5 red balls and 6 blue balls. A ball is drawn randomly, its colour is noted, and then the ball is replaced in the urn. If thisprocess is repeated four times: i. What is the probability of getting two red ba…

a. List the sample space in the given experiment. How many outcomes are 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 rand…

A group of students got the following scores in a test:9,12,15,18,21 and 24. Consider samples of size 3thag can be drawn from this population. List all the possible samples and the corresponding mean. Determine and list all possible s…

Determine the t-value based on the sample size n and a 1)n=25 a= 0.01 Df= T-Value = 2)n=15 a= 0.025 Df= T-Value =

A group of students got the following scores in a test:9,12,15,18,21 and 24. Consider samples of size 3thag can be drawn from this population. List all the possible samples and the corresponding determine and list all possible samples…

indicate whether each of the following statements is true or false. if false indicate why. a) if P(A/B) =0,then A and B are mutually exclusive. b) if P(A/B) =0,then A and B are independent. c) if P(A/B) = P(B/A), then P(A)=P(B). d…

How many four-letter words can be formed using the letters of the word WOMAN?

Is it canbe serve or cannot serve, Explain.P(X) = 3 + X for x = 1, 2, 3, 4 3 – X

P(X) = 1225X for 1, 2, 3, 4

A four-digit number is formed using the digits 1, 2, 3, 5, 8, and 9. What is the probability that the number formed is even?

A pair of dice is rolled thrice. What is the probability of getting doubles in the three rolls?

Determine whether the following can serve as the probability distribution of a random variable X. 1. P(X)= 1/7 for x=1, 2, 3, 4, 5, 6, 7 2.P(X)=x-2/3 for x = 1, 2, 3, 4, 5

If 12% of a population of parts defective, what is the probability of randomly selecting 60 parts and finding that 8 more are defective?

Six women and five men walk into an appliance store at the same time. There are five salesperson available to help them.Find the probability that a salesperson will first help at least 2 women.

Determine the Power set of 𝐴 × 𝐵 if 𝐴 = { 7, 8 } and 𝐵 = { 𝑎, 𝑏 }

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

A coin was flipped four times. Let T be the number of tails that come out. A. Construct the probability distribution of the random variable B.Construct the probability histogram

A large logistic manufacturing company has 100 employees specializing in different machines. From them, 20 are proficient in machine P , 45 in machine Q , 30 in machine R , 1 in machine P and Q , 6 in machine Q and R , 5 in machine R …

1.Find the Domain and Range of the following functions if 𝑓: 𝑅 → 𝑅 i) 𝑓(𝑥) = 12 + 𝑙𝑜𝑔 (1 − 𝑥^2 ) ii) 𝑓(𝑥) = 𝑥^2 +1/𝑥^2 +5 2. Find if the functions are surjective, injective and bijective if 𝑓: 𝑅 → 𝑅 i) 𝑓(𝑥) = 𝑥^5 + 5 ii) 𝑓(𝑥) = 𝑒^4𝑥

What percent of the area under the normal curve is between z=2.25 and z=0.85

Problem 1: School A has a mean population IQ of 100 with a standard deviation of 15. A principal of the said school claims that the students in his school have above average intelligence. A random sample of 30 students IQ scores have …

Laverny tosses an unbiased coin. He receives 100 if a head appears and he pays 40 if a tail appears. Find the variance of his gain.

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. Number of Mobile phone…

Two winners will be drawn from 5 SHS teachers (s) and 7 JHS teachers (J). Let W the random variables representing the JHS teachers. Find the values of the random variable W.

Four coins are tossed. Let M be the variable representing the number of heads that occur. Find the values of the rand om variable M and its corresponding probabilities

The number of patients seen in the emergency room in any hour is a random variable represented by x. Find the probability that in a given hour at least 14 patients will arrive. The probability distribution of x is: *

. From a box containing 4 black balls and 3 green balls, 4 balls are drawn in succession. Let Y be a random variable representing the number of green balls that occur.

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 808 hours and a standard deviation of 93 hours. Find the probability that a random samples of 19 bulbs will have an average life of greater than 799 hours.

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