Sampling Distributions Stats

Employees at a large company can earn monthly bonuses. The distribution of monthly bonuses earned by all employees last year has mean 2.3 and standard deviation 1.3. Let z represent the standard normal distribution. If x represents the mean number of monthly bonuses earned last year for a random sample of 40 employees, which of the following calculations will give the approximate probability that x is less than 2 ?

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Let X be a random variable that has a skewed distribution with mean µ = 10 and standard deviation σ = 10. Based on random samples of size 400, the sampling distribution of X is

• highly skewed with mean 10 and standard deviation 10

• highly skewed with mean 10 and standard deviation 5

• highly skewed with mean 10 and standard deviation 0.5

• approximately normal with mean 10 and standard deviation 10

• approximately normal with mean 10 and standard deviation 0.5

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The Sample

• The Sampling Distribution

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week. Let p-hat be the proportion of people in the sample who attended church. A newspaper report claims that 40% of all U.S. adults went to church last week. Suppose this claim is true.

What is the mean of the sampling distribution of p-hat?

• 0.40

• 0.44

• 0.56

• 0.60

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. 
What is the standard deviation of the sampling distribution?

• 200

• 16

• 25

• 4

The mean weight of potato chip bags is 10.5 ounces with a standard deviation of 3 ounces. A random sample of 40 bags of potato chips is selected. What is the probability that the mean of the sample is less than 10 ounces?

• P = -1.05

• P = .1469

• P = .0202

• P = .8531

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. 
What is the mean of the sampling distribution?

• 200

• 16

• 25

• 4

The average cost for a gallon of gasoline is $2.51 (source AAA.org) with a standard deviation of $0.42. Find the mean and standard deviation of the sampling distribution if n is decreased to 25.

• μ_x-bar = 2.51, σ_x-bar = 0.06

• μ_x-bar = 2.51, σ_x-bar = 0.084

• μ_x-bar = 0.52, σ_x-bar = 0.084

• μ_x-bar = 2.51, σ_x-bar = 0.42

The mean distance an OHS student travels to school is 5.6 miles with a standard deviation of 1.7 miles. Mrs. McLemore finds the mean of her 4th period class - a randomly selected sample of 29 students. What is the probability that the mean of her class is more than 6 miles?

• P = 0.00

• P = 0.1020

• P = 0.8980

• P = 1.27

At a particular college, 78% of all students are receiving some kind of financial aid. The school newspaper selects a random sample of 200 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?

• 78% is a population and 72% is a sample.

• 72% is a population and 78% is a sample.

• 78% is a parameter and 72% is a statistic.

• 72% is a parameter and 78% is a statistic.