Solved: An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 778 hours and a standard deviation of 40 hours. Find the probability that a bulb burns between 710 and 841 hours.

The density function of a random variable X is expressed as f(x) = e^4−xfor x > 4. (a) Find the cumulative distribution function. Determine also the following probabilities. (b)P(X > 6) (c) P(2 ≤ X < 5) …

10. Determine the probability density function for the cumulative distribution function shown below. F {0, x < −2 0.25x + 0.5, −2 ≤ x < 1 0.5x + 0.25, 1 ≤ x < 1.5 1 x > 1.5 Determine also the followin…

Calculate the mean, variance, and standard deviation. Show your solution. 1. X P(X) 1 0.11 2 0.49 3 0.33 4 0.07 2. X P(X) 2 2/10 4 3/10 6 4/10 8 1/10 3. X P(X) 1 0.25 3 0.13 4 0.35 6 …

Two samples consisting of 21 and 9 observations have variances given by s 1 2 =16 and s 2 2 =8 respectively. Test the hypothesis that the first population variance is greater than the second at a (a) 0.05, (b) 0.01 level of signific…

An electronic company in Laguna manufactures resistors that have a mean resistance of 120 ohms and a standard deviation of 13 ohms. Find the probability that a random sample of 40 resistors will have an average resistance greater than…

Count the number of trails in each outcome and assign this number to this outcome

Random Variables Direction: Solve the problem below and complete the table. Suppose three cellphones are tested at random. We want to find out the number of defective cellphones that occur. Thus, to each outcome in the sample spa…

Last year the employees of the city health department donated an average of $ 8 to the rescue squad. Test the hypothesis at the 0.01 level of significance that the average contribution this year is still $ 8 if a random sample of 35 e…

Determine the mean, variance and standard deviation of the probability mass fucntion: X: 0,1,2,3,4 P(x): 0.1, 0.2, 0.3, 0.3, 0.1 thanks!!!

Two balls are drawn in succession without replacement from an urn containing 5 orange balls and 6 violet balls. Let V be the random variable representing the number of violet balls 0 orange balls. Find the values of the random variabl…

A jeepney can accommodate 16 passengers. If x denotes the number of male passengers in the jeepney when it is full, what are the possible values of x?

In a normal distribution 41% of items are under 55 and 11% are over 66. Find the mean and variance of the distribution.

Given that P(X=2)=8P(X=4)+80P(X=46) for a Poisson distribution variate X. Find 1) P(X<2) 2) P(X>4) 3) P(X>=1)

A researcher is conducting a survey about the cellphones used by 50 employees. If � represents the number of users of Brand X, what are the possible values of �? (2 points

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…

Find the probability that a pitcher throws 9 perfect innings in a row, assuming the pitcher's performance in any one inning is independent of his performance in other innings.

Use emperical rule to complete the following table. Write on the respective range or interval of the scores based on the given parameters. Draw the normal curve for each item. Mean Standard 68% 95% 99.70% Deviation 1. 63 …

Each month, a Filipino household generates an average of 30 pounds of garbage for recycling. Assume that the distribution is normal with a standard deviation of 2 pounds. If a household is selected at random, find the probability of i…

last year the employees of the city health department donated an average of $ 8 to the rescue squad. test the hypothesis at the 0.01 level of significance that the average contribution this year is still $ 8 if a random sample of 35 e…

Suppose that the standard deviation of the tube life of a particular brand of TV picture tube is known to be 500, the population of tube life cannot be assumed to be normally distributed. However, the sample mean of x = 8900 is base…

In 2015, the mean return of all common stocks on the Philippine Stock Exchange was 0.45. The standard deviation of the returns was about 6.2. A student of finance forms all possible portfolios that invested equal amounts in 4 of these…

Given the population mean of 12, and a sample standard deviation of 3 in a sample size of 125 𝑛 = ______ 𝜇 = ______ 𝑠 = ______ 3. A population composed of 11 items whose measurements are 12…

Conduct a hypothesis test to determine if these data provide convincing evidence that the average score varies across some (or all) groups. Check conditions and describe any assumptions you must make to proceed with the test. [5 point…

If three mangoes are taken one after the other from a basket which contain 10 ripe and 4 unripe mangoes 1. What is the probability that you will get 3 ripe mangoes? 2. What is the probability that you will get 2 ripe mangoe…

IX is uniformly distributed over the interval [0,10], compute P{2

Need help on this problem. Use the method of moment to estimate the parameter θ for the density f(x; θ) = 1/θ I[0, θ)(x)

A generalised random walk is given by dS = a(x,t)dt + b(x,t)dW where a(x,t),b(x,t) are given functions of space and time and dW is a Weiner process i.e. and is a random number normally distributed with a mean of 0 and a variance…

A box contain 3 dimes, 3 nickels and 1 penny .3 coins are being selected at random without replacement .(Where 1 Dime=10 cent, 1 Nickle=5 cent and 1 penny=1 cent)

4. A generalised random walk is given by dS = a(x,t)dt + b(x,t)dW where a(x,t),b(x,t) are given functions of space and time and dW is a Weiner process i.e. and is a random number normally distributed with a mean of 0 and a varia…

For example seven use three small stripes.what is the largest three digit number that you can make if you use twenty stripes

Supposed three cellphones are tested at random. Let D represent the defective cell phone and N let represent the non-defective cell phone. If we let X be the random variable for the number of defective cell phone, construct the probab…

define the random variable 𝑌 to the absolute value of the difference between the two rolls. What is the probability mass function?

A TELCO office has seven telephone lines. For the past months, the probability distribution of the random variable X which represents the number of busy lines per day, X={0, 1, 2, 3, 4, 5, 6, 7} P(X)={.02, .27, .06, .22, .15, .04, .08…

The average expenditure per student (based on average daily attendance) for a certain school year was $10,337 with a population standard deviation of $1560. A survey for the next school year of 150 randomly selected students resulted …

Four coins are tossed. Let H be the random variable representing the number of the heads occur. Find the values and construct the probability distribution of the random variable H.

Using the Z table, find the critical value for a) α = .05, two-tailed test b) α = .01, two tailed test c) α = .10, two-tailed test

The average expenditure per student (based on average daily attendance) for a certain school year was $10,337 with a population standard deviation of $1560. A survey for the next school year of 150 randomly selected students resulted …

What is the probability that the number of pants sold is more than 3

Find the variance for the sample given in a. 2, 4, 7, 12, 15

let the random variable x represent the number of boys in the family construct the probability distribution for the family of two children

Two balanced dice are rolled. Let X be the sum of two dice. Obtain the probability distribution of X

Four coins are tossed together and the random variable S gives the number of tails that will appear.

Suppose a coin is tossed two times. Let T be the random variable representing the number of tails that occur. Find the values of the random variable T and construct its probability distributions.

a group of students got the following scores in an achievement test:9,12,15,18,21,and 24.consider sample of size 3 that can be drawn from this population A. determine and laser the possible samples and the corresponding sample …

Find the mean of the following probability of a random variable X. P(1) = 1/8 , P(2) = 3/8, P(4) = 3/8, P(4) = 1/8

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

find the mean of the probability distribution of the random variable x, which can take only the values if P(x)= 1/10 , for x= 1,2,3...., 10

Ron tossed unbiased coin, on each toss, he wins P50 if head appears, and loses P40 if tail appears. What will be the expected value of his gain?

Draw the normal curve, then locate the given z values in the curve. Find the area that corresponds to the given z values using the z-table, then shade the required area.

A population consistent of value 3,5,7 and 9 1)List all the possible of size n=3 when drawing with replacement and compute the mean of each sample 2) construct a sampling distribution of the mean 3) compute …

A teacher gets the height of each student in his class,and it has the mean of 161 cm and a standard deviation of 10cm Approximately what percent of these student have a height greater than 164 cm?

A basket contains 12 ripe and 7 unripe mangoes. If four mangoes are taken from the basket one after the other, how many samples space we have in this experiment?

What can you assume if the graph of a distribution is bell-shaped?

Suppose three coins are tossed. Let Y be the random variable representing the number of tails that occur. Find the values of the random variable Y

A meeting of consuls was attended by 4 Americans and 2 Germans. If three consuls were selected at random one after the other, illustrate the probability distribution of a random variable G (number of Germans) and draw the histogram.

Four coins are tossed.Let Z be the random variable representing of heads that occur.Construct a table and find the values of random variable Z. 1.Determine the sample space.Let represent the tail and it represent the head. 2.Count t…

Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of Blue balls. Find the values of the random variable Z

Find the probability given the following z-scores. Use figure 1. For this activity

Suppose three coins are tossed. Let Y be the random variable representing the number of heads that occur. Find the probability of each of the values of the random variable Y completele the table below

Consider the population consisting of 1, 2, 3, 5, 6, and 7. Suppose samples of size 4 are drawn from this population. Describe the sampling distribution of the sample means. Compute for the mean and the variance of the sampling distri…

Medical aid board wants to find if the mean time to settle medical claims of members differs between 2 major medical schemes. The sample mean time to settlement was 10.8 days. Population standard deviation of 3.2 days for 1 and the ot…

6. A shipment of five computers contain two that are slightly defective. If a retailer receives three of these computers. How many random variables X representing the number of slightly defective computers? a. 1 b. 2 c. 3 d. 4

Medical aid board wants to find if the mean time to settle medical claims of members differs between 2 major medical schemes. The sample mean time to settlement was 10.8 days. Population standard deviation of 3.2 days for 1 and the ot…

Find 𝑷(𝟐) and the value of 𝒌 in the following discrete probability distribution. Show your complete solution x=0,1,2,3,4 p(x)=0.13,0.27,𝒌,0.09,0.12 (a) find 𝒌 (b) 𝑷(𝟐)

80 score in percentage

Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 74.4 Mbps. The complete list of 50 data speeds has a mean of x=18.26 Mbps and a standard deviation of s=22.09 Mbps…

A certain kind of sheet metal has, on average, 9 defects per 14 square feet. Assuming a Poisson distribution, find the probability that a 25 square foot metal sheet has at least 14 defects. Round your answer to four decimals.

The number of typographical errors per page typed by a certain typist follows a Poisson distribution with a mean of 17. Then find the probability p that the total number of errors in one randomly selected page is 13. Round your answ…

A company prices its tornado insurance using the following assumptions: • In any calendar year, there can be at most one tornado. • In any calendar year, the probability of a tornado is 0.02. • The number of tornadoes in any calend…

John is offering chocolates at a Plaza. The experimental probability of a randomly chosen shopper accepting a sample is 10%. The conditional probability of a customer purchasing some chocolates given that he/she tried the sample is 18…

Find the missing Value in each of the following Mean X standard deviation Z 1. 60 72 8 2.58 72 2 3.45 3.2 1 4.77 56 7

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 probabil…

A sample of 25 elements from a normally distributed population is selected.the sample mean is 10.assuming a population standard deviationog 4, determine the 95%confidence interval for mean ?

the weights of 1000 children have average of 45 kilograms and a standard deviation of 5 kilograms, how many children weight 35 kg to 55 kg

You play a game with two six-sided dice. If you roll a sum of 3 or 8, you win ₱600. If you roll a sum of 10, you win ₱400. However, you lose ₱500 for anything else. If you continue to play the game, how much do you expect to win o…

In a hospital, a statistician records the sex of newborn babies. Let M be the random variable representing males among five newborn babies.

In a certain country, the true probability of baby being a girl is 0.45. Among the next seven randomly selected births in this country, what is the probability that at least one of them is a boy? Would it be a significant event if…

A machinist is making engine parts with axle diameters of 0.700 inch. A random sample of 10 parts shows a mean diameter of 0.742 inch with a S.D. of 0.040 inch. Compute the statistic you would use to test whether the work is meeting t…

A basket contains 12 ripe and 7 unripe mangoes. If four mangoes are taken from the basket one after the other, how many samples space we have in this experiment?

Daniel went to the perya and played a game. The rule says that the outcome of the game is a random variable from 1 to 14 and that if the outcome is even, he wins ₱50. If the outcome is odd, he wins nothing. Assuming that playing i…

X 3 6 9 12 15 P(X) 4/9 2/9 1/9 1/9 1/9

Two balls are pick in succession without replacement, 4 white balls and 5 green balls. let Y be the random variable representing tge gree balls. Find the values of a random variable Y. Complete the table gelow.

If you believe that your brand of refrigerator last longer than the mean of 14 years...

suppose that you are searching for a room for rental at makweng until you find a place that will satisfies your needs. Suppose that the probability of finding the right place is 0.4. what is the probability that you do not choose at l…

If X follows a normal distribution with u = 30 and o = 4, what is P(X <27)?

A psychologist feels that playing soft music during a test will change the results of the test...

Monthly food expenditures for families in Rodriguez Rizal averaged Php6,500 w a standard deviation of Php750. Assuming that the monthly food expenditures are normally distributed. What percentages of these expenditures are betwe…

a pair of fair dice is rolled. let x the random variable is representing the sum of the numbers that appear

construct the probability distribution of X for a pair of dice

The number of calories in a certain dessert is normally distributed with a mean of 210 and a standard deviation of 12. Find the probability that the dessert one select will contain between 185 and 216.

The score of Entrance Examination takers who took a 600 item exam resemble a normal distribution with a mean of 220 and a standard deviation of 10. The coordinator would like to get the lowest 15% of the scores and invite them f…

The absolute value of the difference of the squares of numbers that turn up when a pair of fair dice is rolled.

The number of females employees selected if five employees are selected by lottery from a group of six male and six female employees.

The professional organization for private colleges and universities professors reported that more than 17% of professors attended a national convention in the past year. To test this claim, a researcher surveyed 2…

The professional organization for private colleges and universities professors reported that more than 17% of professors attended a national convention in the past year. To test this claim, a researcher surveyed 200 pro…

The school registrar estimates that the dropout rate of freshmen high schools in Mindanao is 20%. Last year, 45 freshmen from a random sample of 250 Mindanao freshmen high school withdrew. At 𝛼 = 0.01, is there enough ev…

A survey of Davao Region finds the average commute time of employees on one way is 30 minutes. The Digos Chamber of Commerce feels that in their city is greater and want to publicize this. They randomly select 28 commuters and f…

Let X be a random variable with the following probability distribution: x 1 2 3 4 P(X) 0.4 0.3 0.2 0.1 Find the expected value and variance.

The school registrar estimates that the dropout rate of freshmen high schools in Mindanao is 20%. Last year, 45 freshmen from a random sample of 250 Mindanao freshmen high school withdrew. At 𝛼 = 0.01, is there enough evidence t…

An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 778 hours and a standard deviation of 40 hours. Find the probability that a bulb burns between 710 and 841 hours.

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