It is estimated that 55% of the freshmen entering a particular college will graduate from that college in four years. a. For a random sample of 5 entering freshmen, what is the probability that exactly 3 will graduate in four years? b. For a random sample of 5 entering freshmen, what is the probability that a majority will graduate in four years? c. 80 entering freshmen are chosen at random. Find the mean and standard deviation of the proportion of these 80 that will graduate in four years.

It is estimated that 55% of the freshmen entering a particular college will graduate from that college in four years. a. For a random sample of 5 entering freshmen, what is the probability that exactly 3 will graduate in four years? b. For a random sample of 5 entering freshmen, what is the probability that a majority will graduate in four years? c. 80 entering freshmen are chosen at random. Find the mean and standard deviation of the proportion of these 80 that will graduate in four years.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Sixty percent (60%) of all computers sold by a large computer retailer are laptops. (The remaining…

A: From the provided information,60% of all computers sold by a large computer retailer are laptops…

Q: Of all the registered automobiles in Colorado, 10% fail the state emissions test. Nine automobiles…

A: Probability, p =10% Sample size, n = 9

Q: in a certain region, the mean annual salary for electricians is $58,650. Let x be a random variable…

A: GivenMean(μ)=58650standard deviation(s)=1890sample size(n)=40

Q: Given a normal population whose mean is 665 and whose standard deviation is 24, find each of the…

A: The following information has been given: The population mean is μ=665. The population standard…

Q: Given a normal population whose mean is 325 and whose standard deviation is 73, find each of the…

A: GivenMean(μ)=325standard deviation(σ)=73

Q: Assume that different groups of couples use a particular method of gender selection and each couple…

Q: One thousand people compete in an oyster-eating contest. Their scores (number of oysters eaten) are…

A: According to the given information, we haveThe mean of the distribution is The standard deviation of…

Q: At a large publishing company, the mean age of proof readers is 36.2 years, and the standard…

A: A z-score describes the position of a raw score in terms of its distance from the mean, when…

Q: A random sample of n = 100 scores is selected from a population. Which of the following…

A: We have given thata random sample of n = 100 scores is selected from a populationWe have to identify…

Q: Assume that different groups of couples use a particular method of gender selection and each couple…

Q: In an certain species of newt, offspring are born either green or black. Suppose that 45% of these…

A: The mean of the sampling distribution of the sample proportion. The standard deviation of the…

Q: There are 225 dogs that participated at the National Dog Show that weigh an average of 5 kilos, with…

Q: The weekly salaries of 5,000 employees of a large corporation assumed to be normally distributed…

A: P(480<X<530)=?

Q: a. Find the mean and the standard deviation for the numbers of girls in groups of 16 births. The…

A: Different groups of couples use a particular method of gender selection and each couple gives birth…

Q: 44% of students in a class have black hair. If 66 students are chosen at random, what is the…

Q: 2. According to Eckhoff University statistics, the probability that any of its students is married…

A: Given The probability that any of its students is married=30%sample size =23

Q: Assume that different groups of couples use a particular method of gender selection and each couple…

Q: The population mean for the average weigh of 12 year old children is 102 pounds and the population…

A: Solution: Let X be the weight of 12 year old children. From the given information, µ=102 pounds,…

Q: In an certain species of newt, offspring are born either green or black. Suppose that 60% of these…

A: Given Information:Sample proportion() = 60% =0.6Sample size (n) = 185

Q: According to The World Bank, only 9% of the population of Uganda had access to electricity as of…

Q: The probability that an individual is right-handed is 0.87. In a class of 100 students, what is the…

Q: Use a normal approximation to find the probability of the indicated number of voters. In this case,…

A: given data p = 0.22 n = 131 P(x=32) = ? use normal approximation of binomial distribution.

Q: Construct all random samples consisting two observations from the given data. You are asked to guess…

A: Given information: Watermelon A, B, C, D, E, and F has a weight (in pounds) 19, 14, 15, 9, 10 and 17…

Q: High school girls average 80 text messages daily. Assume the population standard deviation is 15…

A: Given information:

Q: A jar contains 11 red marbles, 12 blue marbles, and 6 white marbles. Four marbles from this jar are…

A: Geometric Distribution: Let there is a sequence of trials, each having two outcomes, say Success and…

Q: In an certain species of newt, offspring are born either green or black. Suppose that 60% of these…

A: Given Information: p = 60% Sample size (n) = 144

Q: The probability that a patient recovers from a delicate heart operation is 60%. There are 20…

A: Formula : Binomial distribution is given by

Q: Four coins are tossed. Let Z be the random variable representing the number of heads that occur.…

A: Given: Four coins are tossed. The random variable Z denotes the number of heads that occurs.

Q: Assume that different groups of couples use a particular method of gender selection and each couple…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: Consider a binomial distribution. About 35% of all college students are currently enrolled in an…

A: Given : Probability of success = p = 0.35 Number of sample = n = 25

Q: Given a normal population whose mean is 580 and whose standard deviation is 38, find each of the…

A: The question is about normal distribution Given : Popl. mean of a normal dist. ( μ ) = 580 Popl.…

Q: iven a normal population whose mean is 580 and whose standard deviation is 77, find each of the…

A: Given that μ=580,σ=77

Q: An automatic machine in a manufacturing process is operating properly if the lengths of an important…

Q: From a batch of bushings made per shift by a turner, 10 pieces are randomly selected for control.…

A: Total pieces is 30, 25 are first grade and 5 are second grade. A random sample of 10 is selected.

Q: Given a normal population whose mean is 350 and whose standard deviation is 47, find each of the…

A: Let us denote the variable by X. Given that X follows a normal distribution with mean= 350 and…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

It is estimated that 55% of the freshmen entering a particular college will graduate from that college in four years.
a. For a random sample of 5 entering freshmen, what is the probability that exactly 3 will graduate in four years?
b. For a random sample of 5 entering freshmen, what is the probability that a majority will graduate in four years?
c. 80 entering freshmen are chosen at random. Find the mean and standard deviation of the proportion of these 80 that will graduate in four years.

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Employers want to know which days of the week employees are absent in a five- day work week. Most employers would like to believe that employees are absent equally during the week. Suppose a random sample of 60 managers were asked on which day of the week they had the highest number of employee absences. The results were distributed as in the data below. For the population of employees, do the days for the highest number of absences occur with equal frequencies during a five-day work week? Test at a 5% significance level. State the null hypothesis, the alternative hypothesis, the p value and whether you will reject or not reject the hull hypothesis. Number of Absences Expected Number of Absences Monday Tuesday Wednesday Thursday Friday 15 12 9 15 12 12 9 12 12 12
3.A school conducted an IQ test to 32 randomly selected students. The standard deviation in the same group of students is 13, and the population mean is 300. What is the probability that the average test score in the sample group will be at the most 315? A.0.82 B.1 C.0.59 D.0.79
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 48 couples. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of girls in groups of 48 births. The value of the mean is μ =. (Type an integer or a decimal. Do not round.) The value of the standard deviation is o = (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. Values of girls or fewer are significantly low. (Round to one decimal place as needed.) Values of girls or greater are significantly high. (Round to one decimal place as needed.) c. Is the result of 34 girls a result that is significantly high? What does it…
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 48 couples. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of girls in groups of 48 births. The value of the mean is u = %3D (Type an integer or a decimal. Do not round.) The value of the standard deviation is o = (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. Values of girls or fewer are significantly low. (Round to one decimal place as needed.) Values of girls or greater are significantly high. (Round to one decimal place as needed.) c. Is the result of 44 girls a result that is significantly high? What does…
Q2. Among a group of five people selected at random from a certain population it is known that the probability that no one will be 35 or over 0.01024.i. What is the probability that exactly one person in the group is under 35?ii. Calculate the mean and variance of the probability distribution of the number of persons over 35 and compare to the formula values for this type of distribution.iii. Given three such groups, what is the probability that two out of three groups have no more than two persons 35 or over?
Twenty-five percent of the employees of a large company are minorities. A random sample of 7 employees is selected. a. What is the probability that the sample contains exactly 4 minorities? b. What is the probability that the sample contains not more than 2 minorities? c. What is the standard deviation of the minorities?
A normal population has a mean of 65 and a standard deviation of 6. You select a random sample of 64. a. Compute the probability that the sample mean is greater than 64 b. Compute the probability that the sample mean is less than 63 c. Compute the probability that the sample mean is between 63 and 64.
Suppose you sample 2 students from every classroom where a class is being held at Duke University at around 12 PM and gather data on their current GPAs. Research from Duke University says that the average GPA is 2.9 with a standard deviation of 0.3. Suppose this is true. What is the probability that a random sample of 15 students will have a sample mean of 3.0 or less? a. None of these b. 99% c. 90% d. 63% e. Cannot be solved since the sampling distribution cannot be established.
A population proportion is 0.59. Suppose a random sample of 656 items is sampled randomly from this population. Appendix A Statistical Tables a. What is the probability that the sample proportion is greater than 0.61?b. What is the probability that the sample proportion is between 0.58 and 0.60?c. What is the probability that the sample proportion is greater than 0.58?d. What is the probability that the sample proportion is between 0.53 and 0.56?e. What is the probability that the sample proportion is less than 0.50?
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.Assume that the groups consist of 41couples. . a. Find the mean and the standard deviation for the numbers of girls in groups of 41 births.
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 47 couples. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of girls in groups of 47 births. The value of the mean is μ = . (Type an integer or a decimal. Do not round.) The value of the standard deviation is o =. (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. Values of girls or fewer are significantly low. (Round to one decimal place as needed.) Values of girls or greater are significantly high.. (Round to one decimal place as needed.) c. Is the result of 44 girls a result that is significantly high? What does…
A survey asks a random sample of 1500 adults in Ireland if they support an increase in the plastic bag levy. Let p˄ denote the proportion in the sample that says they support the increase. Suppose that 30% of all adults support the increase. The standard deviation of the sampling distribution is?