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WorksheetsCentral limit theorem for Mean (Averages)- Practice quiz
Total questions: 20
Worksheet time: 1hrs 10mins
What is the relationship between the mean of the population and the mean of the sampling distribution of the sample means?
the mean of the population is greater than the mean of the sampling distribution of the sample means.
the mean of the population is lesser than the mean of the sampling distribution of the sample means.
the mean of the population is equal to the mean of the sampling distribution of the sample means.
the mean of the population is not equal to the mean of the sampling distribution of the sample means.
What have you observed with the histogram of the sampling distribution of the sample mean?
The histogram is skewed to the left, regardless of the shape of the population.
It will tend to have an abnormal distribution, regardless of the shape of the population.
The bar in the histogram will be equally distributed
It will tend to have a normal distribution, regardless of the shape of the population.
Consider a population with μ=50 and σ=5 is taken. Find the mean of the sampling distribution of the sample mean with a sample size of 30.
50
25
20
5
Consider a population with μ=50 and σ=5 is taken. Find the standard deviation of the sampling distribution of the sample mean with a sample size of 30.
5
0.91
0.71
0
The population mean age of the residents in a certain city is 56.12 years with a standard deviation of 15.3 years. A group of 2000 residents from a certain barangay in the city is taken as a sample. If the population of the city 150 000, find the mean of the sampling distribution of the sample mean of the residents’ ages.
150 000
2 000
15.3
56.12
The population mean age of the residents in a certain city is 56.12 years with a standard deviation of 15.3 years. A group of 2000 residents from a certain barangay in the city is taken as a sample. If the population of the city 150 000, find the standard deviation of the sampling distribution of the sample mean of the residents’ ages.
150 000
0.34
0.5
56.12
What is the standard error of the sampling distribution?
What is the probability of selecting 25 data values with a mean less than 190?
A customer service department monitors how long their callers wait on hold before being helped. The time spent by the callers on hold follows a normal distribution similar to this:
Suppose that we took random samples of 30 callers and calculated the sample mean time spent on hold for each sample of customers. We can assume that the callers in each sample are independent.
What would be the shape of the sampling distribution of the sample mean?
Skewed to the left
Skewed the right
Approximately normal
Unknown, there is not enough information to determine
Let X be a random variable with mean μ=20 and standard deviation σ=4. A sample of size 64 is randomly selected from this population. What is the approximate probability that the sample mean X of the selected sample is less than 19?
(give your answer to 4 decimal places)
(a)
In the first semester of the year 2003, the average return for a group of 251 investing companies was 4.5% and the standard deviation was 1.5%. If a sample of 40 companies is randomly selected from this group, what is the approximate probability that the average return of the companies in this sample was between 4% and 5% in the first semester of the year 2003?
(give your answer to 3 decimal places)
(a)
A population of 29-year-old males has a mean salary of $29,321 with a standard deviation of $2,120. If a sample of 100 men is taken, what is the probability their mean salaries will be less than $29,000?
give your answer to 2 decimal places
(a)
In a recent study reported Oct. 29, 2012, on the Flurry Blog, the mean age of tablet users is 34 years. Suppose the standard deviation is 15 years. Take a sample of size n = 100.
Find the 95th percentile for the sample mean age (to one decimal place).
(a)
