Solved: A sample of 60 Grade 11 students' ages was obtained to estimate the mean of all Grade 11 students. The sample mean is 16.4 years and the population standard deviation is 4. What is the point estimate for µ?

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

As studied, the average number of hours spent by senior high school students for their online classes a week is 25 hours with a standard deviation of 4 hours. Assuming that the study is is true and the data is normally distributed.

What is the probability of getting a sum that is multiples of 3 when two dice are thrown?

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. construct a sampling distribution of the resulting sample means

A box contains 58 red marbles, 14 yellow marbles, and 28 blue marbles. All the marbles are of the same size. Three marbles are drawn at random from the box, first one, then a second, and then a third. Determine the probability of gett…

between z= -1.36 and z= 2.55

b. If one car is randomly chosen, find the probability that it is traveling more than 78 mph

Find the mean of the probability distribution of the random variable x, which can take only the values 1, 2, and 3. Given that P(1) = 10/33, P(2) = 1/33, and P(3) = 12/33

A basket contains 8 ripe (R) and 6 unripe (U) bananas. If three bananas are taken from the basket one after the other with replacement. Construct table that shows all the possible outcomes of the random experiment and all the values o…

P(z>-2.14)

Suppose three cell phones are tested at random where D represent the defective cell phone and N represent the non-defective cell phone. Let X represents the number of defective cell phones that occur. , show the values of the random v…

Samples of size 3 are taken from the population 7, 8, 3, 4, 5, 6, 9, 2, 1 with replacement and without replacement. Find (1) The mean and standard deviation of the population. (u The mean of each of the sampling distribution of mea…

find the mean of the probability distribution of the random variable x, which can take only the values 1,2 and 3, given that P(1)= 10/33 P (2) =1/33 and P(3)= 12/33

x=1,3,4,5,10 P(X=x)= 0.30, 0.20, 0.10, 0.15, 0.25 Question: a. What is the range of the variable x? b. What is P(3

Global insurance has found that 20% (1 in 5) of all insurance policies are surrendered (cashed in) before their maturity date. Assume that 10 policies are randomly selected from the policies data base What is the probability that: …

The random variable X represents the number of taxi cabs a doctor meets on his way to the hospital. The probability distribution of X is given in the following distribution table. X P(x) 0 0.01 1 0.15 2 0.20 3 0.25 …

Identify the following as discrete or continuous random variables. (a) Q: Total number of points scored in a football game (b)R: Shelf life of a particular drug (c) S: Height of the ocean’s tide at a given location (d)T: T…

Wood paneling can be ordered in thickness of 1/16,1/8,1/4, or3/8inch. The random variable X is the total thickness of paneling in two orders. List the elements in the sample space.

A key ring contains four office keys that are identical in appearance, but only one will open your office door. Suppose you randomly select one key and try it. If it does not fit, you randomly select one of the three remaining k…

Past experience has shown that, on the average, only one in ten wells drilled hits oil. Let X be the random variable that represents the number of drillings until the first success (oil is struck). Assume that the drillings …

A company has 7 applicants, three women and four men. Suppose that the 7 applicants are equally qualified and that no preference is given for choosing either gender. Let X be the random variable described by the number of wo…

Global insurance has found that 20% (1 in 5) of all insurance policies are surrendered (cashed in) before their maturity date. Assume that 10 policies are randomly selected from the policies data base What is the probability that: …

a) Consider a consulting firm in a particular city where past records show that on average 6 customers arrive daily to seek consulting services. The demand for consulting services in the firm is distributed according to a Poisson dis…

a) A movie producer is bringing out a new movie. In order to map out his advertising campaign, he wants to determine whether the movie will appeal most to a particular age group or whether it will appeal equally to all age groups. Th…

Question Three Three different fertilizers were applied to twenty plots and the yields were recorded as follows. A 21 4 30 25 14 B 8 8 12 5 3 8 5 28 10 10 C …

A regional hardware chain is interested in estimating the proportion of their customers who own their own homes. There is some evidence to suggest that the proportion might be around 0.70. Given this, what sample size is required if…

Use the five step process to determine each of the following areas 1. Between z = 0 and z = 2.67 2. Between z = -0.78 and z = -1.95 3. Between 1.27 and z = -2.1 4. To the right of z = 0.33 5. to the Left z = 1.96

Four coins are tossed. Let Y be the random variable representing the number of tails that occur. Find the values of the random variable Y . Construct a probability distribution.

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

1. 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.

The probability that a patient recovers from a delicate heart operation is 0.9. The next 100 patients having this operation, find the probability that (i) between 84 and 95 (inclusive values) survive? (ii) fewer than 86…

three coins are tossed let h be the random variable when head will occur.find the values of the random variable H

A meeting of envoys was attended by 5 koreans and 3 filipinos. if four envoys were selected at random one after the other, determine the values of the variable K representing the number of koreans.

on a final examination in biology, the mean was 75 and the standard deviation was 12. determine the standard score of a student who received a score of 60 assuming that the scores are normally distributed.

1. 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 mass…

The height of learners (in cm) at a high school can be described by the N(174.50,47.61) distribution. If 1000 learners are randomly selected from the school, how many of them would you expect to have a height of less than 160.0 cm?

A short-term insurance company receives seven motor vehicle claims, on average, per day. Assume that the daily claims rate follows a Poisson process. Calculate all the probabilities using the Poisson formula What is the probability t…

Suppose the time spent by a randomly selected student at a campus computer lab has a gamma distribution with mean 20 minutes and variance 80 minutes.

A population consists of the four numbers 1, 2, and 4. List all the possible samples of size n=2 which can be drawn replacement from the population. Find the following a.) Population means b.) Population Variance c.) Popula…

Below is an incomplete probability distribution for a random variable X. x 1 2 3 4 5 6 f(x) 0.15 0.25 0.33 0.09 (a) If f(4) = P(X = 4) = 2P(X = 5), complete the probability distribution above. (b)Construct a pr…

A deck of 52 playing cards has 4 aces. The probability of getting one ace less than zero

Verify whether f(x) = (8/7) (1/2)^x , x = 1,2,3 is a probability mass function. If it is, determine the following probabilities. (a) P(X ≤ 1) (b)P(X > 1) (c) P(2 < X < 6) (d)P(X ≤ 1 or X > 1)

From the probability mass function f(x) =2x+1/25 for x = 0,1,2,3,4, find the cumulative distribution function of the random variable X. Using F(x), determine the following probabilities. (a) P(X ≤ 1) (b)P(2 ≤ …

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.

A sample of 60 Grade 11 students' ages was obtained to estimate the mean of all Grade 11 students. The sample mean is 16.4 years and the population standard deviation is 4. What is the point estimate for µ?

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