1. The distribution of scores on the SAT is approximately normal with a mean of μ = 500 and a standard deviation of σ = 100. For the population of students who have taken the SAT: What proportion have SAT scores greater than 685?
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. The distribution of scores on the SAT is approximately normal with a mean of μ = 500 and a standard deviation of σ = 100. For the population of students who have taken the SAT:
What proportion have SAT scores greater than 685?
Include the 0 before the decimal point and leave four places after the decimal point
2. The distribution of scores on the SAT is approximately normal with a mean of μ = 500 and a standard deviation of σ = 100. For the population of students who have taken the SAT:
What is the minimum SAT score needed to be in the highest 30% of the population?
B. If the state college only accepts students from the top 80% of the SAT distribution, what is the minimum SAT score needed to be accepted?
3. A consumer survey indicates that the average household spends µ = $185 on groceries each week. The distribution of spending amount is approximately normal with a standard deviation of σ = $25. Based on this distribution.
B. What proportion of the population spends more than $250 per week on groceries?
Include the 0 before the decimal point and leave four places after the decimal point
4. A consumer survey indicates that the average household spends µ = $185 on groceries each week. The distribution of spending amount is approximately normal with a standard deviation of σ = $25. Based on this distribution.
B. What proportion of the population spends less than $100 per week on groceries?
Include the 0 before the decimal point and leave four places after the decimal point
5. A consumer survey indicates that the average household spends µ = $185 on groceries each week. The distribution of spending amount is approximately normal with a standard deviation of σ = $25. Based on this distribution.
B. How much money do you need to spend on groceries each week to be in the top 20% of the distribution?
Include the 0 before the decimal point and leave four places after the decimal point
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