Solved: An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 811 hours and a standard deviation of 95 hours. Find the probability that a random samples of 44 bulbs will have an average life of less than 799 hours.

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.

In a certain town, 40% of the eligible voters prefer candidate A, 10% prefer candidate B, and the remaining 50% have no preference. You randomly sample 10 eligible voters. What is the probability that 4 will…

The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by x 01234 f(x) 0.41 0.37 0.16 0.05 0.01 Construct the cumulative distribution func…

Two independent samples of sizes 8 and 7 contained the following values: Sample I : 19 17 15 21 16 18 16 14 Sample II : 16 14 15 19 15 18 16 Do the estimates of the population variance differ significantly at 5% level?

Assume Y is discrete random variable with probability distribution. { 0.2ky+ 0.1 , for y=0,1,2,3,4 P(Y=y) = { 0 , elsewhere Using R programming, apply the suitable coding to identify answer in (a),(b). (a) probability distr…

The table below shows the weight of 21 students (on the left) and the corresponding number of students with that weight (on the right). Compute the Mean of the data below. Weight No. of Students 34 5 39 8 43 2 45 6

Instruction: Solve the following problem. Find and construct the: Sample space (all outcomes) Possible values Properties 1 and 2 Probability Mass Function Histogram 1. Number of Blue balls Four balls are drawn in succession wit…

A basket contains 5 white ball (w) and 5 black ball (b). What is the possible result if you draw 3 balls in random from the basket.let x be the random variable representing the number of black ball that occur.

Refer to Example 8. How large a sample will we need in order to assert with probability 0.95 that the sample mean will not differ from the true mean by more than 1.5. (replacing σ by s is reasonable here because the estimate is ba…

Question 1 In the Monty Hall Problem described by Karl, the correct approach when confronting to the decision of changing or keeping the door is to... Option: never change the door to increase the probability of winning the pri…

how to find the variance and standard deviation of a discrete random variable

A BASKET CONTAINS 5 WHITE BALL (W) AND 5 BLACK BALL (B). WHAT IS THE POSSIBLE RESULT IF YOU DRAW 3 BALLS IN RANDOM FROM THE BASKET. LET X BE THE RANDOM VARIABLE REPRESENTING THE NUMBER OF BALCK BALL THAT OCCUR.

Construct the probability distribution of a particular experiment by following the instructions given to you. A dog gave birth to a litter of six puppies. Three of them are male while the rest are female.if you are to be given th…

The geometric mean of a group of 15 observations was calculated as 12. It was later found that one observation was wrongly read as 19 instead of the correct value 9. Obtain the correct geometric mean of the data.

n 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 below 45

One of the city's professional football teams (team 1) plays at home and another (team 2) plays away on the same night. A professional football a 0.641 probability of winning a home game and a 0.462 probability of winning an away game…

Mr. Vijay, a retired government servant, is considering investing his money in two proposals. He wants to choose the one that has higher average net present value and lower standard deviations. The relevant data are given below. Can y…

A survey conducted by U.P research institute on the retrenchment exercise done by the result when a random sample of 10 ministries were selected from a population that is normally distributed, show the following number of workers that…

Using the sample space for rolling two dice, illustrates a probability distribution for random variable X respending the sum of the number that appear

Nigeria population consist of three major ethnic group Yoruba(Y), Hausa (H) and Ibo(I), which make up 30%, 60% and 10% of the population respectively. A sample of 80people includes 21from Yoruba, 57 from Hausa and 2 from Ibo. Is there…

Given the computed mean value, µ = 85 and the standard deviation, σ = 5, convert the following raw scores to its z-scores: a.) x = 92

What is the probability of getting an ace when a card is drawn from a deck of cards?

number of computers sold per day at a local computer store are 0,1,2,3, and 4 with the probabilities 0.1, 0.2, 0.3, 0.2, and 0.2 respectively. Find the variance and standard deviation of the distribution

1.It is claimed that the average weight of babies at birth is 3.4 kg. The average weight of a random sample of 30 newly born babies was determined.It was found out that the average weight was 3.1 kg. Is there a reason to believe that …

Probability mass function consists of the values a random variable can assume and the corresponding probabilities of the values.

What is the chance of getting a sum of prime number when the sum of two dice are rolled?

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 811 hours and a standard deviation of 95 hours. Find the probability that a random samples of 44 bulbs will have an average life of less than 799 hours.

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