Solved: examples of Functions (Continuity and inverse of a function),

The time taken to assemble a car in certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability the car can be assembled at this plant in a period of time a…

Five hundred children participated in a field demonstration. Their heights averaged 110 cm with a standard deviation of 6 cm, a. What is the probability that a child, picked at random, has a height greater than 116 cm? b. What is t…

Given a standard normal distribution with mean =101 and standard deviation = 43, find P(X>145)

Given a standard normal distribution with mean =61 and standard deviation = 35, find P(X<113)

Given a standard normal distribution with mean =115 and standard deviation = 30, find P(X<85)

An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 817 hours and a standard deviation of 48 hours. Find the probability that a bulb burns between 736 and 823 hours.

The weights of 1,000 children, in average, is 49kg with standard deviation of 18kg. Suppose the weights are normally distributed, how many children weigh between 53kg and 59kg?

The weights of 1,000 children, in average, is 61kg with standard deviation of 10kg. Suppose the weights are normally distributed, how many children weigh less than 60kg?

I. SAMPLE SPACE AND RANDOM VARIABLES Direction: With the experiments below, tabulate the data you gathered and find their sample space and random variable. Show your complete solution. (20 points total) 1. Tossing a coi…

The weights of 1,000 children, in average, is 62kg with standard deviation of 19kg. Suppose the weights are normally distributed, how many children weigh greater than 56kg?

An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 809 hours and a standard deviation of 48 hours. Find the probability that a bulb burns between 728 and 848 hours

I. SAMPLE SPACE AND RANDOM VARIABLES Direction: With the experiments below, tabulate the data you gathered and find their sample space and random variable. Show your complete solution. (20 points total) 1. Tossing a coin four…

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.

Use the following cell phone airport data speeds (Mbps) from a particular network. Find P80.

A box contains 6 red balls, 5 blue balls, and 10 green bas. In how many ways can you choose 2 red balls and 5 green balls

1. One of the undersecretary of the Department of Labor and Employment (DOLE) claims that the average salary of Social worker is Php18, 000. A sample of 19 social worker’s salary has a mean of Php17, 350 and standard deviation of…

The heights of 100 students are normally distributed with a mean height of 16 centimeters and standard deviation of 5.9 centimeters. Answer the following in percent form. a. How many of these students would you expect to hav…

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 786 hours and a standard deviation of 80 hours. Find the probability that a random samples of 17 bul…

4. The probabilities that a printer produces 0, 1, 2, and 3 misprints are 42%, 28%, 18%, and 12%, respectively. Construct the probability Mass function and then compute the mean value of the random variable.

a. Find the pdf of x = [a b] a 2-d vector, where a is a Bernoulli random variable and b is a Gaussian random variable. Assume, θ is the parameter for Bernoulli which gives the probability of a = 1, that is p(a=1) = θ. Assume, b foll…

A bag contains 8 blue and 7 yellow balls. Two balls are drawn in succession without replacement. Find the probability that both the balls are of yellow color.

Studied nine subjects who underwent baffle procedure for transposition of greater artery.at baseline the systemic vascular resistant measured is WU×m2 value at rest yielded a standard deviation of 28.test the hypothesis if we can conc…

There is a bag filled with 4 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 of the same …

Hemoglobin(g percent) values were recorded for a sample of 20 children who were part of a study of acute leukemia. The varience of the observation is 5 test the hypothesis if this data provide sufficient evidence to indicate that the …

The range of the sample data is what Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. Given that these are the top 10 s…

Find number of students securing marks >104, between 155-165, <55 from the following class data. Class(marks) frequency (students) 0-20 210 20-40 115 40-60 130 60-80 220 80-100 120 100-…

v> Dr Mukonda has two cars, which he hires out day by day. The number of demands follows poisson with mean 1.5. Calculate the probability that on a day: (a) Neither car is used (b) Some demands is refused.

an investigator predicts that dog owners in the country spend more time walking their dogs than do dog owners in the city. the investigator gets a sample of 21 country owners and 23 city owners. the mean number of hours per week that …

a) Find the appropriate rejection regions for the large-sample z-test in these cases: i) A right-tailed test with \alphaα = 0.01; ii) A two-tailed test at 5% signi cance level; iii) A left-tailed test with \alphaα = 0.05.…

In a normal distribution, 69% of the distribution is less than 28 and 90% is less than 35. Find the mean and standard deviation of the distribution

The length of Paulo’s lunch break follows a normal distribution with mean u and standard deviation 5 minutes. On one day in four, on average, his lunch break lasts for more than 52 minutes. (i) Find the value of u.

a) i) Suppose H0: \muμ = \muμ 0 is rejected in favour of H1 : \muμ != \muμ 0 at \alphaα = 0.05 level of signifi cance. Would H0 necessarily be rejected at the \alphaα = 0.01 level of signi cance? Explain.…

The length of Paulo’s lunch break follows a normal distribution with mean u and standard deviation 5 minutes. On one day in four, on average, his lunch break lasts for more than 52 minutes. (i) Find the value of u. (ii) Find the proba…

b) two types of engines, A and B, were compared. Gas mileage, in miles per gallon, was measured. 50 experiments were conducted using engine type A and 75 experiments were done with engine type B. The gasoline used and other conditions…

Part 1. Choose the correct answer and write the letter responding to it on the answer sheet. 1. The type of graph for grouped frequency distribution that plot marks against frequency A. O gives B. Vertica…

P(z>2.92)

6. Given a set of n numbers which of the following is not changed by adding a non-zero constant to each of the numbers. A. the median B.the mid-range C.the arithmetic mean D.the standard devation 7. From…

P(-3.10

a) A manufacturer has developed a new shing line, which the company claims has mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilograms. To test the claim, a random sample of 50 lines will be tested. The rejec…

Let T be a random variable giving the number of heads in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and assign a value to each sample point.

. Let T be a random variable giving the number of heads in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and assign a value to each sample point.

the fraction of defective items in a large lot is ‘p’. to test the null hypothesis h0: p=0.2, one consider the number ‘f’ of defectives in a sample of 8 items and accept the hypothesis if f≤6, and reject the hypothesis otherwise. what…

a) The weight (in ounces) of a frozen food package produced by a given manufacturer is a normal random variable with mean \muμ and variance \sigmaσ2 (both unknown). We weigh n = 10 of these packages, selected at random and…

9. The following statements are true except, the A, sum of the probabilities of two complementary events of a statistical experiment is 1. B, sum of the probabilities of all the sample points of a statistical experiment is 1. C. …

In a recent study, it is found that a person in a city has a 40% chance of being infected by the flu virus. 20% of those who have been infected with the virus are symptoms free while 10% of those who are not infected show th…

Suppose you toss a coin 100 times and get 66 heads and 34 tails. Based on these results, what is the probability that the next flip resuming a tail

WORKOUT PROBLEMS Instruction: show all the necessary steps for the following problems on the space provided. 2. If two members are chosen at random from a committee consisting of 10 members of which 4 are women. Then what is the pro…

Two cubical dice are thrown and their scores addes together if X= add is the sum of the scores on the two dice what is P(X is divided by 4)

At a tennis tournament, a statistician keeps track of every serve. The statistician reported that the mean serve speed of a particular player was 87 miles per hour (mph) and the standard deviation of the serve speeds was 13 mph. Assum…

Two random samples gave the following data. ni-10, n-12, mean of sample 1-15,mean of sample 2-14 sum of squares of the deviations from the mean of samples are 90,108.Can we conclude that the two samples have been (13) drawn …

A coin tossed and die is rolled. The outcome of the coin is recoded "1" when it shows a head, and "0" when it shows a tail. The random variable gives the sum of the outcomes of coin and die. Compute the average val…

A random sample of size 16 has 53 as mean. The sum of the squares of the deviation taken from mean is 150. Can this sample be regarded as taken from the population having 56 as mean? Obtained 95% and 99% level of con…

An investigator predicts that dog owners in the country spend more time walking their dogs than do dog owners in the city. The investigator gets a sample of 21 country owners and 23 city owners. The mean number of hours …

In a corcert, 1684 were sold out to teenagers and 792 were sold to adults. Estimate p and q for the population of teenagers and adults who bought tickets to the concert.

During field trip joined by 800 pupils, 610 took the rides provided by the school . Find p and q , where p was the population of children who took the rides

5. A class in statistics contains 10 students, 3 of whom are 19, 4 are 20, 1 is 21, 1 is 24, and 1 is 26. Let X be the average age of the 2 randomly selected students and derive the probability function for X. …

The brain volumes (cm3) of 20 brains have a mean of 1052.9 cm3 and a standard deviation of 121.3 cm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or …

.A box contains four blue and three red marbles. Michelle picks four marbles at random from this box. If Z is the random variable representing the number of blue marbles picked from the box, construct the probability di…

A population consists of the four members 6,9,15,18. Consider all possible samples of size two which can be drawn with replacement from the population. Find population mean, the standard deviation and the mean of the sampling di…

You are given a population with standard deviation of 8.6. Determine the sample size needed to estimate the mean of the population with error of 0.5 at 99 percent confidence.

A group of 5 patients treated with Medicine type A weight 42, 39, 48, 60 and 41 kg. A second group of 5 patients treated with Medicine type B weight 38, 42, 48, 67, 40 kg. Do the two medicines differ significantly with regard to…

A group of 5 patients treated with Medicine type A weight 42, 39, 48, 60 and 41 kg. A second group of 5 patients treated with Medicine type B weight 38, 42, 48, 67, 40 kg. Do the two medicines differ significantly with regar…

A random sample of size 16 has 53 as mean. The sum of the squares of the deviation taken from mean is 150. Can this sample be regarded as taken from the population having 56 as mean? Obtained 95% and 99% level of confidence limi…

Population 1 consists of the values 5, 7, and 9. Population 2 consists of values (1, 5). Consider all the possible samples of size 2 that can be drawn with replacement from population 1 and all the possible samples of size 3 that can …

Find number of students securing marks >104, between 155-165, <55 from the following class data. Class(marks) frequency (students) 0-20 210 20-40 115 40-60 13…

The following data shows heights in centimeters of 10 persons selected at random from a village. Find out whether, it would be reasonable or justifiable to suppose the height of that village population as 182 cm. The heights …

A presidential candidate asks a polling organization to conduct a nationwide survey to determine the percentage of potential voters who would vote for him over his rival presidential candidate. Out of 2 500 respondents, 915 said that …

11. Find z if the standard normal-curve area a) between 0 and z is 0.4726; b) to the left of z is 0.9868; c) to the left of z is 0.3085; d) between -z and z is 0.9282 12. If a random variable has…

The number of taxis waiting at a cab stand is thought to follow a uniform distribution. The number present was recorded at 50 random times:Use the appropriate goodness of fit test to determine if the uniform distribution is a good ch…

Construct a probability distribution table if we let X the random variable be the number of boys in the family with 3 children.

The variance of the number of cars sold per day is 2.27 what is the Standard deviation of the cars per day?

Nikbakht has received an email from an unknown mailer offering an entry into a lottery. For a price, he can get a ticket that may pay a prize double the price. He buys 2 tickets. Unknown to him an unfair system determines a winner whe…

From the past experience of software quality testing, it is known that the probability of the presence of an error in coding is 0.05. If the probability of a tester detecting an error when the error is present is 0.78 and the probabil…

The local government is planning to give financial assistance to low income families in remote barangays due to COVID-19 crisis. To be successful in this endeavor, the mayor instructed his staff to conduct a survey in order to de…

A random sample of size 50 is drawn from binomial distribution with parameters n=100 and p=0.3. what is the probability that the sample mean is a)larger than 3.9 b) between 4.1 and 4.4 c) smaller than 4.0

A basket contains 10 ripe and 4 unripe bananas. If three bananas are taken from the basket one after the other, determine the possible values of the random variable U representing the number of unripe bananas

A simple random sample of 10 people from a certain population has a mean age of 27. Can we conclude that the mean age of the population is not 30? The variance is known to be 20.

The mean monthly sale of a particular household item in department stores was observed as 133.3 units per store. After an advertising campaign, data on sales of this item from 25 stores were collected and it is found that the mean sal…

A statistician is studying blood pressure levels of Italians in the age range 75-80. The following is some information about her study: The data were collected by responses to a survey conducted by email, and no measures …

1. Daily sales records for a car dealership show that it will sell 0, 1, 2, or 3 cars, with probabilities as listed: Number of Repairs(X) 0 1 2 3 p(x) 0.5 0.3 0.1 0.1 …

a factory is manufactures face masks that widely used during pandemic covid-19. it is found that on average, 10% of the face masks produced are defective. if 150 face masks are randomly selected, what is the probability that the numbe…

Assume that random guesses are made for seven multiple choice questions on an SAT test, so that there are n=7 trials, each with probability of success (correct) given by p=0.55. Find the indicated probability for the number of corr…

wenty samples each of size 10 were inspected. The number of defectives detected in each of them is given below: 0, 1, 0, 3, 9, 2, 0, 7, 0, , 1, 0, 0, 3, 1, 0, 0, 2, 1, 0 Find the control limits for the nu…

Determine the probability of drawing an even-numbered card or a card with a red suit from a standard deck of cards. Leave your answer in a reduced fraction.

True or False. (i) Age of a student is a discrete data. (ii) Mean is not affected by extreme values. (iii) A histogram can not be made for categorical data. (iv) ∑ 5 20 7 = 70. (v) The spread of a single value is always zero. (v…

construct the probability distribution of the random variable for the given situation. Two balanced diced are rolled. Let S be the random variable denoting the sum of the number of dots that will appear

An operation is carried out by a subsystem consisting of three units that operate in a series configuration. (a) The units have exponentially distributed lifetimes with mean 1. How many subsystems should be operated in parallel to a…

The officer's of the science club are planning to sell 125 tickets to be raffled during the school's foundation day . One ticket will win PHP 2,000 and the other tickets win nothing. If you buy one ticket, what will be your expected g…

if random variable is uniformly distributed (-2,1) find pdf of y = 2x ^3

Consider a population consisting of 5 units with the following values of a variable Y: 29, 87, 94, 10, 13. A simple random sample of size 3 is picked from this population without replacement. i. Write down all the possible simple rand…

Two coins are tossed. Let T be the number of tails that occurs. Determine the values of the random variable T. Three coins are tossed. Let T be the number of tails that occurs. Determine the values of the random variable T. A meeting …

Compute the probabilities using the standard normal curve P(-1.89 < z < 1.68)

2) Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The following table shows the shipping costs per truck…

examples of Functions (Continuity and inverse of a function),

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Question ID: mtid-4-stid-46-sqid-1769-qpid-239