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7-2 (Vocab)
7-3
7-4
7-5
7-6
100
What is a continuous, symmetric, bell-shaped distribution of a variable?
It is a normal distribution.
100
z = ?
z = (value - mean)/ standard deviation
100
If the scores for the test have a mean of 100 and a standard deviation of 15, find the percentage of scores that will fall below 112.
78.81% or the scores fall below 112.
100
What is the difference between the sample measure and the corresponding population measure due to the fact that the sample is not a perfect representation of the population.
It is the sampling error.
100
N x p = ?
N x p = mean
200
What question is answered by the normal distribution curve?
It answers the question, "What is normal?"
200
Find the area under the normal distribution curve between z=0 and z=2.34.
The area is 0.4904 or 49.04%
200
Each month, an American household generates an average of 28 pounds of paper waste. Assume the standard deviation is 2 pounds. If a household is selected at random, find the probability of it generating more than 30.2 pounds per month.
The probability is 0.1357 or 13.57%
200
A report says that children watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3 hours. If 20 children are randomly selected, find the probability that the mean number of hours they watch television will be greater than 26.3 hours.
It is 2.62%
200
A magazine reported that 6% of American drivers read the newspaper while driving (YIKES!). If 300 drivers were selected at random, find the probability that exactly 25 say they read the newspaper while driving.
The probability is 2.27%
300
What is more important in applied statistics under a normal distribution curve - the area or the frequencies?
The areas are more important.
300
Find the area to the right of z = 1.11.
The area is 0.1335 or 13.35%
300
An exclusive college desires to accepts only 10% of all graduating seniors based on a test. The test has a mean of 500 and a standard deviation of 100. Find the cutoff score for the exam. Assume the variable is normally distributed.
The scores of 628 is used as a cutoff.
300
The average number of pounds of meat a person consumes a year is 218.4 pounds. Assume that the standard deviation is 25 pounds and the distribution is approximately normal. If a sample of 40 individuals is selected, find the probability that the mean of the sample will be less than 224 pounds per year.
The probability is 92.22%
300
Of the members of a bowling league, 10% are widowed. If 200 bowling league members are selected at random, find the probability that 10 or more will be widowed.
The probability is 99.34%
400
When the majority of data values fall to the right of the mean, what is it called? How about to the left?
Negatively skewed. Positively skewed.
400
Find the area between z= 1.68 and z= -1.37.
The area is 0.8682 or 86.82%
400
For a medical study, a researcher wishes to select people in the middle 60% of the population based on blood pressure. If the mean systolic blood pressure is 120 and the standard deviation is 8, find the upper and lower readings that would qualify people to participate in the study.
The middle 60% would have readings of 113.28 < X < 126.72
400
The average weight of a group of young adult males is 160 pounds. The standard deviation is 10 pounds. If a sample of 30 people is selected from the population of 300, find the probability that the mean will be less than 156 pounds.
The probability is 1.04%
400
If a baseball player's batting average is 0.320 (32%), find the probability that the player will get at most 26 hits in 100 times at bat.
The probability is 0.1190 or 11.9%
500
What are 5 of the properties of the theoretical normal distribution? Note: There are 8 properties.
1. The normal distribution curve is bell-shaped. 2. The mean, median, and mode are equal and located at the center of the distribution. 3. The normal distribution curve is unimodal (i.e. it has only one mode) 4. The curve is symmetrical about the mean, which is equivalent to saying that its shape is the same on both sides of a vertical line passing through the center. 5. The curve is continuous - i.e. there are no gaps or holes. 6. The curve never touches the x axis, although it gets increasingly closer. 7. The total area under the normal distribution curve is equal to 1.00 or 100%. 8. The area under the normal curve that lies within one standard deviation of the mean is approximately 0.68, or 68%.
500
Find a z value to the left of the mean so that 96.86% of the area lies to the right of it.
It is -1.86
500
In a certain normal distribution, 1.25% of the area lies to the left of 42 and 1.25% of the area lies to the right of 48. Find the mean and standard deviation.
The mean equals 45 and the standard deviation equals 1.34.
500
The standard deviation of a variable is 15. If a sample of 100 individuals is selected, compute the standard error of the mean. What size sample is necessary to double the standard error of the mean?
1.5. n=25.
500
A political candidate estimates that 30% of the voters in his party favor his proposed tax reform bill. If there are 400 people at a rally, find the probability that at least 100 favor his tax bill.
It is 0.9875.