Mean and Standard Deviation from Probability Distribution

It is the standard deviation symbol

• σ

• X

• N

The average speed of 1500 vehicles traveled on a stretch of highway that day is 67 miles per hour with a standard deviation of 3.5 miles per hour. If 100 vehicles are randomly selected as samples, what would be the mean of the resulting sampling distribution of sample means?

• 63.5

• 67

• 70.5

• 74

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?

• -1.05

• .146

• .020

• .853

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 39 students. What is the probability that the mean of her class is more than 6 miles?

• 0.002

• 0.070

• 0.898

• 1.27

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 = 0.0251, σ_x-bar = 0.06

• μ_x-bar = 2.51, σ_x-bar = 0.857

In one region of the country, the mean length of stay in hospitals is 5.5 days with standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, x, recorded for each sample. Which of the following is the best description of the sampling distribution of x ?

• Strongly skewed to the right with mean 5.5 days and standard deviation 2.6 days

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.26 day

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.026 day

• Approximately normal with mean 5.5 days and standard deviation 2.6 days

• Approximately normal with mean 5.5 days and standard deviation 0.26 day

A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

• 0.1151

• 0.2743

• 0.7257

• 0.8849

• Based on the values of the true mean and true standard deviation, it can be concluded that the population distribution is not normal and therefore the probability cannot be calculated.

The normal probability distribution is completely described by its mean and ________.

• variance

• standard deviation

• range

• mean deviation

By standardizing a normal probability distribution, we can report the distance of a value from the mean in units of the __________ .

• median

• standard deviation

• variance

• mode

The standard normal probability distribution has mean of 0 and a standard deviation of _____.