# Quality Answers to a Wide Range of Statistics Questions

Explore quality answers to a wide range of Statistics questions on different topics such as probability, inference, hypothesis, random variables, expectation, variance etc.

- The average monthly salary of 525 public school teachers in a municipality is P18925. 150 public school teachers were interviewed and found out they are receiving an average monthly salary of P17000. Identify the following: 1. Popula…
- A box contains 5 balls. One is numbered 1, three are numbered 2, and one is numbered 3. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is rep…
- The manufacturer of the Horizon truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. Assume the mileage wear follows the normal distribution and the standard deviation of the distr…
- A labor union claims “40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job were available” 74 persons out of the 200 sampled said they would return to work. Can we conclud…
- There are two octahedral dice with faces marked 1 through 8. They are constructed such that the side 8 is 1.5 times as probable as the 2 through 7 and the sum of the probabilities of the 1 and the 8 equals that of the pairs on opposin…
- Suppose two dice was rolled. Let Y be the random variable representing the number of even number that occur. Find the values of the random variable Y.
- For each of the following scenarios, give an example of a discrete and a continuous random variable. The first one is done as an example. Scenarios •Asking your classmates about their breakfast. •Making an order at a fast food r…
- Among 250 employees, of the local office of an international insurance company, 182 are whites, 51 are blacks and the rest are Orientals. If 5% margin of error is used, 5. How many employees will be chosen for a case study as sample…
- Given \mu=118, \sigma=29μ=118,σ=29 then, p(76\lt x\lt 144)=p({76-118\over29}\lt Z\lt{144-118\over29})=p(-1.45\lt Z\lt 0.90)p(76
- A population is normally distributed with a population mean of 76 and a population standard deviation of 13. i. State the distribution of the sample mean for simple random samples of size n = 100. ii. Given a simple random sample …
- Given a standard normal distribution with mean =78 and standard deviation = 28, find P(85 < X < 102)
- Given a standard normal distribution with mean =118 and standard deviation = 29, find P(76 < X < 144)
- Given a standard normal distribution with mean =136 and standard deviation = 39, find P(X>84)
- Suppose a particle moves along the x-axis beginning at 0. It moves one integer step to the left or right with equal probability. What is the probability function of its position after four steps?
- Suppose a fair die is tossed two times. Let X be the larger of the two faces that appear. Find px(k).
- Given a standard normal distribution with mean =62 and standard deviation = 44, find P(X>92)
- Given a standard normal distribution with mean =58 and standard deviation = 40, find P(X<96)
- A man has four keys in his pocket and, since it is dark, cannot see which is his door key. He will try each key in turn until he finds the right one. Let X be the number of keys tried (including the right one) to open the door. Wha…
- Given a standard normal distribution with mean =60 and standard deviation = 35, find P(X<75)
- An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 814 hours and a standard deviation of 42 hours. Find the probability that a bulb burns between 747 and 846 hours.
- 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.
- An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 799 hours and a standard deviation of 49 hours. Find the probability that a bulb burns between 769 and 878 hours.
- The weights of 1,000 children, in average, is 50kg with standard deviation of 14kg. Suppose the weights are normally distributed, how many children weigh between 53kg and 68kg?
- The weights of 1,000 children, in average, is 46kg with standard deviation of 20kg. Suppose the weights are normally distributed, how many children weigh less than 63kg?
- The weights of 1,000 children, in average, is 55kg with standard deviation of 17kg. Suppose the weights are normally distributed, how many children weigh greater than 38kg?
- A random sample of size 144 is drawn from a population whose distribution, mean, and standard deviation are all unknown. The summary statistics are x−−=58.2 and s = 2.6.
- Let XX be a random variable represented by the sum of the outcomes, There are 4^2=164 2 =16 possible outcomes with replacement 2: (1, 1)2:(1,1) 3: (1, 2), (2, 1)3:(1,2),(2,1) 4: (1, 3), (2, 2), (3, 1)4:(1,3),(2,2),(3,1) 5: (1, 4…
- A box contains 5 balls. One is numbered 1, three are numbered 2, and one is numbered 3. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is rep…
- •Box A and B contains 1, 2, 3, 4. Construct the probability distribution and draw a histogram of the sum when one number from each box is taken with placement
- How many ways 6 delegates to the convention from a group of 24 qualified students
- Random samples of size n were selected from binomial populations with population parameters p given here. Find the mean and the standard deviation of the sampling distribution of the sample proportion ^p = X \bar in each case: …
- In how many ways can a teacher select 6 delegates to a national convention from a group of 24 students
- The scores for a mathematics course seem to be normally distributed with mean 70 & standard deviation of 8. If the instructor wishes to give an A grade to 10% of the students, what should be the dividing line between an A grade and a …
- suppose the weight of 800 students are normally distributed with mean 75kg and standard deviation 5kg. find the numer of students that weigh more than 80kg
- Suppose that the bank customers arrive randomly and independently on an average of 3.2 customers every 4 minutes. What is the probability that: a. Exactly two customers arrive in every 4 minutes? b. Exactly two customers will arriv…
- Oranges chosen at random have a mean mass of 210 grams and standard deviation of 35 grams. Assuming a normal distribution, what is the probability of choosing an orange with a mass between 170 grams and 250 grams
- To compare the results of boys and girls in a class, a special test was given to 50 boys who averaged 67.4 with Sd. of 5.0, and 50 girls averaged 62.8 with Sd. of 4.6. (Group Assignment) (2 pts.) a) Test, at …
- To compare the results of boys and girls in a class, a special test was given to 50 boys who averaged 67.4 with Sd. of 5.0, and 50 girls averaged 62.8 with Sd. of 4.6. (Group Assignment) (2 pts.) a) Test, at 0.05 …
- A manufacturer of paper used for packaging requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour's production…
- Let X be a binomial(5, 0.2) random variable. Let Y be a discrete random variable that is independent of X, such that Y = 1 with probability 0.2 and Y = 0 with probability 0.8. What is the probability that the sum of X and Y is less th…
- A dataset has a mean of 15 km and a standard deviation of 2 km with n equal to 30. There is a mode of 22 km and a median of 18 km with a range of 20 km. What is the variance?
- According to a hospital administrator, historical records over the past 10 years have shown that 20 percent of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospita…
- Four coins are tossed let z e the random variable representing the number of heads that turn up. find the values of the random variable Z
- Supposed five coins are tossed.let x be the random variable representing the number of head occur. Find the probability of each values of the random variable.
- In a railway yard goods trains arrive that at the rate of 30 trains per day. Assuming that the inter-arrival time follows an exponential distribution and the service time distribution is also exponential with an average of 36 mi…
- Using the sample in a family of four children, construct a probability distribution for the variable Z representing the number of boys. Draw the histogram of the probability distribution.
- Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 oranges, with replacement being made after each drawing. Find the probability that (I) Both are white
- A basket contains 10 red balls and 4 white balls. If three balls are taken from the basket one after the other, determine the possible values of the random variable R representing the number of the red balls
- A shipment of five computers contains two that are slightly defective. If a retailer receives three of these computers at random, list the sample space using the letters D and N for defective and non-defective computers respectively a…
- A student has to take 7 more courses before she can graduate. If none of the courses are prerequisites to others, how many groups of three courses can she select for the next semester?