Statistics Notes ai
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- Using the standard Normal Table(
- Using z-scores to find Probabilities.
- Using percentiles to find the z-scores.
- Using z-scores to find data
EX. 4 Adult IQ scores are normally distributes with µ=100 and σ= 15. Estimate the probability that a randomly chosen adult has an IQ between 70 and 115. Ex. 5 Estimate the probability that a randomly chosen adult has an IQ between 85 and 145. Ex. 6 Given a normally distributed data set of 500 observations measuring tree heights in a forest what is the approximate number of observations that fall within two standard deviations from the mean?
during a specified interval of time has a mean of 150 and a standard deviation of 10. What percentage of the observed values fall between 140 and 160?
When you have a standard normal distribution, the horizontal scale of the graph of of the standard normal distribution corresponds to z-scores. A z-score is the measure of position that indicates the number of standard deviations a value lies from the mean. 
Looking at the data gathered yesterday from every student’s height, what would be your z-score? Ex 8. Suppose a student sits 2 exams, getting 55 in a verbal test and 60 in a numerical reasoning test. The class scores for each exam are normally distributed. For the verbal test, the mean is 50 and standard deviation 5; for the numerical test, the mean is 50 and standard deviation is 12.What test did he do better on? Using the standard Normal Table(The table gives the value to the left of the number) Ex.9 Find the cumulative area that corresponds to z=3 Ex.10 Find the cumulative area that corresponds to z= -1 Ex.11 Find the cumulative area that corresponds to a z-score of 1.15 Ex.12 Find the cumulative area that corresponds to a z-score of -0.24 Using your calculator normalcdf(lower bound, upper bound, mean, standard deviation) Ex. 13 Team A Quiz Scores = {72, 76, 80, 80, 81, 83, 84, 85, 85, 89} Find the Mean = __________ Standard deviation = __________ z-score for “89”. = ________
Find the Mean = _________ Standard deviation = _________ z-score for “57”. = ________
Using z-scores to find Probabilities. P(x>y) Means the probability of x greater than y. P(x 
EX. 19The lengths of Atlantic croaker fish are normally distributed, with a mean of 10 inches and a standard deviation of 2 inches. An Atlantic croaker fish is randomly selected. Find the probability that the length of the fish is less than 7 inches. Find the probability that the length of the fish is between 7 and 15 inches. Find the probability that the length of the fish is more than 15 inches. Using percentiles to find the z-scores. When the problem gives you the percentile, look in the table to find the percentile closest. This will give you your z-score. To use the calculator, you need to use the invNorm command. invNorm(percentage,mean,standard deviation) Ex. 20 The Welcher Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of 35 and a standard deviation of 6. Assuming these raw scores form a normal distribution: What number represents the 65th percentile (what number separates the lower 65% of the distribution)? What number represents the 90th percentile? Ex. 21 Scores on the SAT form a normal distribution with  and  .
What is the minimum score necessary to be in the top 15% of the SAT distribution? Find the range of values that defines the middle 80% of the distribution of SAT scores (372 and 628). Using z-scores to find data 
Practice Problems. Donna’s boss asked her to purchase a large number of 20-watt florescent light bulbs for their company. She has narrowed her search to two companies offering 20-watt bulbs for the same price. The Bulb Emporium and Lights-R-Us each claim that the mean lifespan for their 20-watt bulbs is 10,000 hours. The lifespan of light bulbs has a distribution that is approximately normal. The Bulb Emporium’s distribution of the lifespan for 20-watt bulbs has a standard deviation of 1,000 hours and Lights-R-Us’ distribution of the lifespan of 20-watt bulbs has a standard deviation of 750 hours. Donna’s boss asked her to use probabilities associated with these normal distributions to make a purchasing decision. Donna decided that she would compare the proportion of light bulbs from each company that would be expected to last for different intervals of time. She started with calculating the probability that a light bulb would be expected to last less than or equal to 9,000 hours. Letting x represent the lifespan of a light bulb, P(x≤ 9,000 hours) represents the probability that the lifespan of a light bulb would fall less than or equal to 9,000 hours in its normal distribution. Donna continued by finding P(9,000 ≤ x ≤11,000 hours) and P(x ≥11,000 hours) for each company. The ACT® is an achievement test given nationally with normally distributed scores. Amy scored a 31 on the mathematics portion of her 2009 ACT®. The mean for the mathematics portion of the ACT® in 2009 was 21.0 and the standard deviation was 5.3. What percent of the population scored higher than Amy on the mathematics portion of the ACT®?
scored a 720 on the mathematics portion of her 2009 SAT®. Both the SAT® and the ACT® are achievement tests given nationally with scores that are normally distributed. The mean for the mathematics portion of the SAT® in 2009 was 515 and the standard deviation was 116. For the ACT®, the mean was 21 and the standard deviation was 5.3. Whose achievement was higher on the mathematics portion of their national achievement test? Directory: uploads uploads -> 587 Return function, r i(X) r i(0) r i(1) r i(2) r i(3) 1 0 2 4 6 Thermal Station, I 2 0 1 5 6 3 0 3 5 6 10 uploads -> Department of science and humanities department of mathematics part-a questions and answers uploads -> The Case Against the nypd’s Quota-Driven ‘Broken Windows’ Policing What Is It? uploads -> For want of a nail uploads -> Ownership Models There are two different types of ownership models uploads -> Police Militarization uploads -> City of rising star regular meting thursday, july 14, 2016 uploads -> Township of winfield uploads -> Stop Militarizing Law Enforcement Act of 2014 uploads -> The Black Panther Party’s Ten-Point Program What We Want Now! Download 432.92 Kb. Share with your friends:
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