Normal Distribution and Sampling Distributions

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

Calculate μ_x-bar and σ_x-bar if μ = 794, σ = 48, and n = 64

• μ_x-bar = 794, σ_x-bar = 0.75

• μ_x-bar = 12.4, σ_x-bar = 0.75

• μ_x-bar =794, σ_x-bar = 6

• μ_x-bar = 99.25, σ_x-bar = 6

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 error of the sampling distribution if n = 49

• μ_x-bar = 2.51, σ_x-bar = 0.06

• μ_x-bar = 0.358, σ_x-bar = 0.06

• μ_x-bar = 2.51, σ_x-bar = 0.06

• μ_x-bar = 2.51, σ_x-bar = 0.857

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

• The Population

• The Sample

• The Sampling Distribution

A machine fills bottles of shampoo, the amount poured has a mean of 16 oz and standard deviation 0.5 oz. A sample of 30 shampoo bottles has a mean of 15.8 oz. What is the probability of getting a mean weight of less than 15.8 oz?

• 0.99

• 0.66

• 0.34

• 0.01

A machine fills bottles of shampoo, the amount poured has a mean of 16 oz and standard deviation 0.5 oz. A sample of 30 shampoo bottles has a mean of 15.8 oz. What is the probability of getting a mean weight of less than 15.8 oz?

• 0.99

• 0.66

• 0.34

• 0.01

The speed of pickup of ride sharing services like Uber and Lyft seems to have surpassed that of ambulance services. The mean response time of ambulances across the United States is 15.3 minutes with a standard deviation of 12.8 minutes. For ride sharing services, the mean pick-up time across the United States is 8 minutes with a standard deviation of 5.2 minutes. Based on these estimates, which of the following gives the standard deviation of the sampling distribution of the difference in the sample means for samples of 30 ambulance rides and 40 ride sharing rides (Ambulance – Ride Sharing)?

• 
• 
• 
• 
• Cannot be determined because the conditions are not met

Students in a statistics class participated in a project in which they attempted to estimate the true mean height of all students in their large high school. The students were split into 4 groups. Each group had their own sampling method, and they used it to select a sample each day for 50 days. Shown above are the estimates based on their 50 samples. After the samples were collected and the means were plotted the teacher visited the school nurse who told her that the true mean height of all students in the school is 67.5 inches. Which group produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability?

• Group 1

• Group 2

• Group 3

• Group 4

Students in a statistics class participated in a project in which they attempted to estimate the true mean height of all students in their large high school. The students were split into 4 groups. Each group had their own sampling method, and they used it to select a sample each day for 50 days. Shown above are the estimates based on their 50 samples. After the samples were collected and the means were plotted the teacher visited the school nurse who told her that the true mean height of all students in the school is 67.5 inches. Which group produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability?

• Group 1

• Group 2

• Group 3

• Group 4

Researchers are studying populations of two squirrels, the eastern gray and the western gray. For the eastern gray squirrel, about 22 percent of the population weighs over 0.5 kilogram (kg)(kg). For the western gray squirrel, about 36 percent of the population weighs over 0.5 kgkg. A random sample of 60 squirrels will be selected from the population of eastern gray squirrels, and a random sample of 120 squirrels will be selected from the population of western gray squirrels. What is the mean of the sampling distribution of the difference in sample proportions (eastern minus western) ?

Answer explanation

The mean of the sampling distribution of the difference in sample proportions for eastern minus western is equal to the difference in the population proportions, which equals 0.22−0.36