Exam 7: Variation in Repeated Samplessampling Distributions

From the set of numbers {5, 9, 15}, a random sample of size two will be selected with replacement. Determine the sampling distribution of X̄, that is, complete the following table. (Write the probabilities as fractions.)

Suppose the number of passengers in a bus, going from New York City to Washington D.C., is approximately normal with mean 30.4 passengers and standard deviation 1.1 passengers. What proportion of the busses travel with less than 30 passengers?

The daily number of persons who file complaints about the food quality at one fast food location has probability distribution Find the standard deviation of the number of complaints. Round your answer to one decimal place.

The number of students per classroom in a mid-size college is a random variable whose distribution is normal with mean 34 students and standard deviation 4 students. You intend to visit twenty five classrooms, what is the probability that the average number of students per room will be greater than 35.3 students?

Take a random sample of size n = 2, without replacement, from {0, 2, 4, 6}. Let $\bar{x}$ = mean of the two numbers selected. (a) List the six possible $\bar{s}$ amples and the associated value of the sample mean. (b) Construct the sampling distribution of $\bar{x}$ . (c) Obtain the expected value of $\bar{x}$ using the sampling distribu- tion in Part b. (d) Obtain the variance of $\bar{x}$ using the sampling distribution in Part b.

A population has distribution Let X₁ and X₂ be independent and each have the same distribution as the population. (a) Find the expected value and variance of X₁. (b) Determine the missing elements in the table for the sampling distribution of $\bar{X}$ = (X1 + X2) / 2 (c) Find the expected value and variance of $\bar{X}$ . (d) If the sample size is increased to 25, give the mean and variance of $\bar{X}$

In a recent year, 70% of the world's largest companies were foreign

A random sample of size 225 is taken from the population of the ages of seniors enrolled at a large university one semester. This population has mean 22.3 years and standard deviation 2.5. The population distribution is not normal. (a) Is it reasonable to assume a normal distribution for the sample mean $\bar{x}$ Why or why not? (b) Find the probability that $\bar{x}$ lies between 22.1 and 22.5 years. (c) Find the probability that $\bar{x}$ exceeds 22.7 years.

The daily number of persons who file complaints about the food quality at one fast food location has probability distribution What is the approximate probability that this fast food location will receive more than 140 complaints in a period of 100 days?

A numerical feature of a population is called a ______.

The heights of male students at a university have a nearly normal distribution with mean 70.5 inches and standard deviation 2.8 inches. If 5 male students are randomly selected to make up an intramural basketball team, what is the probability that the heights of the team averages over 72.0 inches?