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Sampling Distribution for a Mean

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Wize University Statistics Textbook > Sampling Distribution

Sampling Distribution for a Mean

4 Activities

In a certain city, the income level of its residents follow the normal model with mean $40,000 and standard deviation $18,000. A resident is considered wealthy if he/she earns more than $60,000.

A random sample of 400 residents is drawn from this city. Find the probability that more than 15% of them are wealthy.
More Sampling Distribution for a Mean Questions:
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean Question
Sony is interested in the number of songs on a person’s iPhone. The population distribution of songs is normal with a mean of 300 and a standard deviation of 60.
(a) What’s the probability that a random iPhone will have more than 375 songs?
(b) If Sony randomly samples 12 iPhones, what’s the probability that the sample mean will be more than 375 songs?
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that you have a population that's skewed to the left.
You wish to plot the sampling distribution of the sample mean for
all samples of 40 observations.
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling distribution for a mean
Which of the following statements best describes the Central Limit Theorem?
Sampling Distribution for a Mean
Suppose that we look at the height of students at ABC University and know their average height is μ=160 cm\mu=160 \space\text{cm} and vary according to the standard deviation σ=10 cm\sigma=10 \space \text{cm}
What are the mean and standard deviation of the sampling distribution of the sample mean with n = 30 observations?
Sampling Distribution for a Mean
Suppose that the mean height of 5 year old females is 107.9 cm with a standard deviation of 11.1 cm. If height is normally distributed, and you consider a random sample of 10 girls, then the sampling distribution for the corresponding sample mean
Sampling Distribution for a Mean
Suppose that the mean height of 10 year old males is 138.4 cm with a standard deviation of 9.6 cm. From 30 randomly selected 10 year old males, what is the probability the sample mean is greater than 140 cm?
Sampling Distribution for a Mean
The Pogs Fan Club only has 150 members. The number of pogs a member owns is normally distributed with a mean of 265 and standard deviation of 35. What is the probability of selecting a random sample of 10 members with a sample mean of 280 or more?
Sampling Distribution for a Mean
Kick the Butt is interested in the number of cigarettes on a smoker smokes a day. The distribution number of cigarettes is normal with a mean of 15 and a standard deviation of 8.
1. What’s the probability that a random smoker smokes more than 20 cigarettes a day?
2. If they randomly sample 10 smokers, what’s the probability that the sample mean will be more than 13 cigarettes a day?
Sampling Distribution for a Mean
Suppose that we look at the height of students at ABC University and know their average height is μ=160 cm\mu=160 \space\text{cm} and vary according to a standard deviation σ=10 cm\sigma=10 \space \text{cm}. What are the mean and standard deviation of the sampling distribution of the sample mean with n = 30 observations?
Sampling Distribution for a Mean Question
Sony is interested in the number of songs on a person’s iPhone. The population distribution of songs is normal with a mean of 300 and a standard deviation of 60.
(a) What’s the probability that a random iPhone will have more than 375 songs?
(b) If Sony randomly samples 12 iPhones, what’s the probability that the sample mean will be more than 375 songs?
Sampling Distribution for a Mean
The population distribution is skewed to the right. The sample size is 1000. The 95% confidence interval is [$800, $1,200].
True or false: The sample mean must be $1,000.
Sampling Distribution for a Mean
Twin Pines Diner makes mediocre CLT (cabbage, leeks, and turnip) sandwiches. Suppose the average amount of sodium of all CLT sandwiches is 650mg, and the distribution is skewed to the right. If someone randomly samples 200 CLT sandwiches, which of the following is true?
Statistical sampling
Poke Mania can sell an average of 90 poke bowls a day with a standard deviation 7.18; however, the sales are not normally distributed. In fact, the distribution of sales is skewed to the right. Which of the following is true about the sampling distribution of 50 days?
Sampling Distribution
True or false?
If the sample size is large enough, then the sampling distribution of X will be approximately normal, even if the population distribution is quite skewed.