Private nonprofit
1. Private nonprofit four-year colleges charge, on average, $26,367 per year in tuition and fees. The standard deviation is $7,114. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 30,629 per year.
c. Find the 68th percentile for this distribution. $ (Round to the nearest dollar.)
2. Los Angeles workers have an average commute of 30 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 13 minutes. Let X represent the commute time for a randomly selected LA worker. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. Find the probability that a randomly selected LA worker has a commute that is longer than 36 minutes.
c. Find the 85th percentile for the commute time of LA workers. minutes
3.
The average price of a college math textbook is $158 and the standard deviation is $24. Suppose that 49 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For the group of 49, find the probability that the average price is between $157 and $162.
Find the third quartile for the average textbook price for this sample size. $ (round to the nearest cent)
For part b), is the assumption that the distribution is normal necessary? YesNo
The average price of a college math textbook is $158 and the standard deviation is $24. Suppose that 49 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For the group of 49, find the probability that the average price is between $157 and $162.
Find the third quartile for the average textbook price for this sample size. $ (round to the nearest cent)
For part b), is the assumption that the distribution is normal necessary? YesNo
4.
Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 48 minutes and standard deviation 16 minutes. A researcher observed 14 students who entered the library to study. Round all answers to 4 decimal places where possible.
What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
If one randomly selected student is timed, find the probability that this student’s time will be between 49 and 51 minutes.
For the 14 students, find the probability that their average time studying is between 49 and 51 minutes.
Find the probability that the randomly selected 14 students will have a total study time more than 728 minutes.
For part e) and f), is the assumption of normal necessary? YesNo
The top 15% of the total study time for groups of 14 students will be given a sticker that says “Great dedication”. What is the least total time that a group can study and still receive a sticker? minutes
Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 48 minutes and standard deviation 16 minutes. A researcher observed 14 students who entered the library to study. Round all answers to 4 decimal places where possible.
What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
If one randomly selected student is timed, find the probability that this student’s time will be between 49 and 51 minutes.
For the 14 students, find the probability that their average time studying is between 49 and 51 minutes.
Find the probability that the randomly selected 14 students will have a total study time more than 728 minutes.
For part e) and f), is the assumption of normal necessary? YesNo
The top 15% of the total study time for groups of 14 students will be given a sticker that says “Great dedication”. What is the least total time that a group can study and still receive a sticker? minutes
5.
Suppose that the age of students at George Washington Elementary school is uniformly distributed between 6 and 10 years old. 36 randomly selected children from the school are asked their age. Round all answers to 4 decimal places where possible.
What is the distribution of XX? XX ~ U(,)
Suppose that 36 children from the school are surveyed. Then the sampling distribution is
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the probability that the average of 36 children will be between 8 and 8.6 years old?
6.
Sample Solution
Nonprofit organizations play an important role in a country’s social and economic well-being. The majority of nonprofit organizations are tax-exempt under Section 501(c)(3) of the Internal Revenue Code because they help society in ways that the private sector may not. Nonprofit organizations are classified by the Internal Revenue Service (IRS) based on the extent of public involvement in their activities. As a result, nonprofits are divided into two types: public charities (sometimes known as public nonprofit organizations) and private foundations (private nonprofit organizations). The most frequent sort of nonprofit organization classified by the IRS is public charities, or public nonprofit organizations, which is what most people think of when they hear the term “nonprofit.”
