1) In a large high school of 2500 students, the mean number of cars owned by students’ families is 2.35 with a standard deviation of 1.06 cars. a) Think about this distribution. Do you think it is normal? Using the empirical rule give the ranges for each of the 3 standard deviations assuming this is a symmetric and mound shaped distribution. Does it seem like this is the distribution is normal? b) A simple random sample of 16 students is taken and the mean number of cars owned is calculated. What are the mean and standard deviation of the sample mean? Can we use this to find probabilities? Why or why not? c) A simple random sample of 36 students is taken and the mean number of cars owned is calculated. What are the mean and standard deviation of the sample mean? Can we use this to find probabilities? Why or why not?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
1) In a large high school of 2500 students, the
a) Think about this distribution. Do you think it is normal? Using the
b) A simple random sample of 16 students is taken and the mean number of cars owned is calculated. What are the mean and standard deviation of the sample mean? Can we use this to find probabilities? Why or why not?
c) A simple random sample of 36 students is taken and the mean number of cars owned is calculated. What are the mean and standard deviation of the sample mean? Can we use this to find probabilities? Why or why not?
d) Using the information in part c) What is the probability that the sample mean is greater than 2.5 cars? Insert the graph from Rguroo that gives the output for this question.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
