. Sunshine City was designed to attract retired people, and its current population of 50,000 residents has a mean age of 60 years and a standard deviation of 16 years. The distribution of ages is skewed to the left.

(a) What is the distribution of the sample mean age of residents for a random sample of 100 residents?

(b) What is the probability that a random sample of 100 residents have a mean age between 50 and 70 years of age?

(c) What is the probability that the mean age of a random sample of 100 residents is less than 55?

### Want to see the full answer?

Check out a sample Q&A here*star_border*

## Related Statistics Q&A

Find answers to questions asked by students like you.

Q: Sunshine City was designed to attract retired people, and its current population of 50,000 residents…

A: Givensample population(n)=50000mean(μ)=60standard deviation(σ)=16

Q: In a study of life expectancy in a certain region, the mean age at death was 70 years, and the…

A: Click to see the answer

Q: 1. What is your estimate of the mean herd size of dairy farms in Northumberland County if a random…

A: Given that μ = 90 , ? = 35 , n = 49 Z-score =(x-μ)/? Note: According to bartleby experts question…

Q: The dean of the business school claims that the average monthly income of his school’s Bachelor of…

A: Given data, μ=24700σ=4100If n=49P(X>23300)=?

Q: The dean of the business school claims that the average monthly income of his school’s Bachelor of…

A: Click to see the answer

Q: According to the American Time Use Survey results released by the Bureau of Labor Statistics on June…

A: Given : μ = 168 , σ= 20 and n= 400 By Central Limit Theorem, x̅ follows a Normal…

Q: According to the American Time Use Survey results released by the Bureau of Labor Statistics on June…

A: From the given information, the mean if 168 minutes and the standard deviation is 20 minutes. That…

Q: The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student…

A: 1000 0.6 600 1000000 600000 1200 0.3 360 1440000 432000 1500 0.1 150 2250000 225000

Q: For a population with a mean of 100 and a standard deviation of of 16, what is the probability that…

A: Given that mean is 100 and standard deviation is 16 That is, μ=100 and σ=16 Sample size, n=4

*question_answer*

Q: Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States.…

A: Obtain the standard Z-score for the random variable X equals 60,000. The standard Z-score for the…

*question_answer*

Q: A report announced that the median sales price of new houses sold one year was $211,000, and the…

A: Sample mean will also follow normal distribution with parameters,

*question_answer*

Q: Suppose the heights of 18 year old men are approximately normally distributed, with mean 71 inches…

A: The normal distribution is the most useful theoretical distribution for continuous variables. For…

*question_answer*

Q: A quality control company was hired to stuudy length company. The team carefully measured the length…

A: Click to see the answer

*question_answer*

Q: A company determined that on an annual basis, the distance traveled per company car is normally…

A: Click to see the answer

*question_answer*

Q: For a population with a mean of 100 and standard deviation of 16, what is the probability that a…

A: The central limit theorem states if the sample size (n) is large (greater than or equal to 30), then…

*question_answer*

Q: The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student…

A: Note: Hey, since multiple questions are posted, we will answer first question for you. If you want…

*question_answer*

Q: The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student…

A: Given data , Admissions (x) P(x) 1000 0.6…

*question_answer*

Q: For a normally distributed population with a mean of 35 and a standard deviation of 7.5, if a sample…

A: From the given information, Mean = 35 Standard deviation = 7.5 The objective is to find the…

*question_answer*

Q: For a normally distributed population with a mean of 35 and a standard deviation of 7.5, if a sample…

A: Given,mean(μ)=35standard deviation(σ)=7.5sample size(n)=50

*question_answer*

Q: Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 56…

A: The Z-score of a random variable X is defined as follows: Z=(X–µ)/σ Here, µ and σ are the mean and…

*question_answer*

Q: The head circumferences of women are normally distributed with a mean of 32 cm and a standard…

A: Mean is 32 and a standard deviation is 9. Sample size 16.

*question_answer*

Q: For a normally distributed population with a mean of 35 and a standard deviation of 7.5, if a sample…

A: The population mean is 35. The population standard deviation is 7.5. The sample size is 50. We have…

*question_answer*

A: Click to see the answer

*question_answer*

Q: A study at a college in the west coast reveals that, historically, 45% of their students are…

A: a) It is known that, the mean of the sampling distribution of sampling distribution, p-hat is equal…

*question_answer*

A: Given Observation and Calculation

*question_answer*

Q: It is known that the distribution of the Wechsler Adult Intelligence test is normal, the mean is µ =…

A: It is given that the mean is 130, the standard deviation is 15 and the sample size is 9.

*question_answer*

Q: Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of…

A: From the provided information, Mean (µ) = 57 Standard deviation (σ) = 3.5 Let X be a random variable…

*question_answer*

Q: Rivers Casino did an audit of all of their blackjack tables and found that the amount of money…

A: Provided information is, Rivers Casino did an audit of all of their blackjack tables and found that…

*question_answer*

Q: For each of the following situations, first determine whether you should use the normal or binomial…

A: It is given that the daily expenses of a family is given as the mean is $247.02 and standard…

*question_answer*

Q: 4. The weights of male basketball players on a certain collegiate basketball league are normally…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

*question_answer*

Q: The salaries at a corporation are normally distributed with an average salary of $19,000 and a…

A: The provided information are: Population mean (µ) = 19000 Population standard deviation (σ) = 4000…

*question_answer*

Q: The reading speed of second-grade students is approximately normal, with a mean of 90 words per…

A: a) The probability that a randomly selected student will read more than 95 words per minute is…

*question_answer*

Q: Household incomes in the city of Tampa Bay are right-skewed with an average of 50,270 and standard…

A: Central Limit Theorem for mean: If a random sample of size n is taken from a population having mean…

*question_answer*

Q: If it is known that the mean time between eruptions at Old Faithful is 96 minutes with a standard…

A: Given that standard deviation of 12 minutes

*question_answer*

Q: 1. The director of admissions at Kinzua University in Nova Scotia estimated the distribution of…

A: Click to see the answer

*question_answer*

Q: Runners in a race have a mean finishing time of 91 minutes and a standard deviation of 16 minutes.…

A: Click to see the answer

*question_answer*

Q: A newspaper publisher has mean sales of 28,200 copies per day with a standard deviation of 3,100…

A: 1. From the given information, the mean sales is 28,200 copies per day and the standard deviation…

*question_answer*

Q: Suppose that the annual household income in a small Midwestern community is normally distributed…

A: Given : X ~ Nμ, σ mean, μ = $55000 S.D, σ = 4500 a. P(household will have an income between $50000…

*question_answer*

Q: what would be the probability that you would select any one individual who falls between +1 and -2…

A: Given that,

*question_answer*

Q: Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 57…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

*question_answer*

Q: Under what circumstances is the distribution of sample means guaranteed to be a normal distribution?

A: A population includes all members from a specified group, all possible outcomes or measurements that…

*question_answer*

Q: Under what circumstances is the distribution of sample means guaranteed to be a normal distribution?

A: Distribution of sample means: The sampling distribution of sample mean follows normal distribution…

*question_answer*

Q: A firm’s marketing manager believes that total sales for next year will follow the normal…

A: Given information- Population mean, µ = $3200,000 Population standard deviation, σ = $250,000 We…

*question_answer*

Q: A spark plug manufacturer claims that the lives of its plugs are normally distributed with a mean of…

A: Let us denote: X= the lives of its plugs X follows a normal distribution with mean=60,000 and…

*question_answer*

Q: 3. For males in a certain town, the systolic blood pressure is normally distributed with a mean of…

A: Click to see the answer

*question_answer*

Q: For a population with a mean of 35 and standard deviation of 7, find the sample mean of size n = 20…

A: The formula to find the sample mean is, x¯=μ+zσn From the Standard Normal Table, the value of z for…

*question_answer*

Q: The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard…

A: Click to see the answer

*question_answer*

Q: The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard…

A: Click to see the answer

*question_answer*

Q: The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard…

A: Click to see the answer

*question_answer*

Q: 1. The scores on a national achievement exam are normally distributed with a mean of 500 and a…

A: Click to see the answer