How Do You Find The Z-Score Of A Percentile And A Given Area Using A Ti-83 Calculator?

From Mathematics Forum:

How do you find the z-score of a percentile and a given area using a TI-83 calculator? Hi I'm having trouble finding the z-score for percentiles and a given area. I use the envenom function on my calculator and it seems to work just fine for the area but sometimes the signs are switched around. I have no idea how to do something like a percentile. An example would be P subscript 3 or 4.

Answer: The inverse of invNorm( is normalcdf(. Simply specify a lower bound and upper bound (between which two z-scores) as arguments (mean and standard deviation are only to be used when working with raw scores) and it will give you the probability. For example, let's say you have some SAT scores data that can be modeled by a Normal distribution with a mean (µ) of 500 and a standard deviation (σ) of 100. 1) Find the percent of scores (area) between 400 and 650. Solution 1: 400 is 1 standard deviation below the mean (z = -1) and 650 is 1.5 standard deviations above the mean (z = 1.5). Into the calculator, type in: normalcdf(-1,1.5) and it should give you .7745375117, which means approximately 77.45% of people score between 400 and 650. Solution 2: An even easier method would be to work with raw scores. Instead, you would type in normalcdf(400,650,500,100), which would, again, give you .7745375117. 2) What percentile is represented by a score of 700? Solution: To do this, you want to know how many people scored below 700 points. So you could type normalcdf(-E99,2) or you could type normalcdf(-E99,700,500,100). The first argument does not have to be -E99 (E can be inserted by pressing [2nd][,](EE)), but it should be a very large negative number. Both ways should give you ≈ 97.72%. Now, invNorm(. invNorm( takes in percentiles and then spits out a z-score (or, if you supply µ and σ, the actual x-value). The reason why the sign is switched is most likely because the question is asking you for the upper percent, but you're calculating for the lower one. Say you had the following question: 3) What score is earned by the worst 15% of test takers? Solution: invNorm(.15) ≈ -1.036 standard deviations below the mean, which corresponds to a score of about 396. Therefore, 15% of test takers scored below a 396. Once again, you could also directly get this number by doing invNorm(.15,500,100). 4) What score is earned by the best 15% of test takers? Solution: if this problem had been first, you would have simply done invNorm(.15), gotten -1.036, and then wondered why the sign was opposite of what it should be. Well, that's because the question is asking for the best, or highest 15%. Therefore, the question could also be asking you what the lowest 85% is, and you'd still get the same answer. So: invNorm(1−.15) ≈ +1.036σ, which is a score of about 500 + 1.036(100) = 603.6 points. Once again, you could have also done invNorm(1−.15,500,100) to get a direct answer of 603.6 points.

How Would I Find The Indicated Z Score, And Draw A Standard Normal Curve That Depicts The Solution?

From Mathematics Forum:

How would I find the indicated z score, and draw a standard normal curve that depicts the solution? Find the z-score that the area under the standard normal curve to its left is 0.1

Answer: Drawing a standard normal curve is fairly simple. You can find many on line. Now use z-score table to find z-score such that P(Z < z) = 0.1 http://www.regentsprep.org/Regents/math/algtrig/ATS7/ZChart.htm The table above shows area to the left of z-scores, which is what you want. The closest value to 0.1 in the table is 0.1003. This is in row −1.2 and column 0.08. So the z-score is −1.28. Now draw vertical line on graph above located at z = −1.28 (about a quarter of the way between −1 and −2). Shade area to the left of this line. This represents area = 0.1 http://www.wolframalpha.com/input/?i=prob%28z%3C-1.28%29

What Is The Z-Score In A Normal Distribution Of Women’S Height Where The Mean Equals 64 Inches And The Stan?

From Mathematics Forum:

What is the z-score in a normal distribution of women’s height where the mean equals 64 inches and the stan? What is the z-score in a normal distribution of women’s height where the mean equals 64 inches and the standard deviation is 3 inches? Please help and offer explanation. thanks so much.

Answer: We're missing information... To find a z-score, we need three things: 1) population mean (μ) 2) standard deviation 3) a given x z-score = (x - μ)/ st. dev For instance, if your problem said: If a randomly chosen women measures 72 inches, what is the z-score in a normal distribution of women’s height where the population mean equals 64 inches and the standard deviation is 3 inches. z-score = (72 - 64) / 3 = 2.67

What Is The Z Score And Do You Reject The Null?

From Mathematics Forum:

What is the z score and do you reject the null? What is the z score and do you reject the null? Information from the Registrar’s Office shows that the GPA for all Arts and Sciences majors is 2.95 with a standard deviation of 0.45. You feel that psychology majors have a higher GPA than the general student body. Your sample of 28 psychology students shows a mean GPA of 3.21.

Answer: null hypothesis: mean µ = 2,95 alternative hyp: mean = µ > 2.95 Sample size = n = 28 st.deviation : 0,45 sample mean = 3.21 z-score = z = (sample mean - µ of null hyp)/(sigma/sqrt(n)) = (3,21 - 2,95)/(0,45/sqrt(28)) = 3,057 The prob-value of the z-score is P(Z > z) = P(Z > 3,057),where Z has a standard-normal distribution. We find P(Z > 3,057) = 0,001 If Alf = 1%, we reject the null

What Is The Formula For Finding The Values On A Z-Score Table?

From Mathematics Forum:

What is the formula for finding the values on a z-score table? Many places tend to direct me to probability distribution tables when I try to find the formula for calculating the actual values on the table. For example: mean = 100 Standard Dev = 15 Raw score = 120 z score = 1.33 On a table, this is no problem to find, but in a scenario when I do not have a table, how do I calculate to find the percentile or (whatever the value of .9082 is called) on the table?

Answer: Do you know integral calculus? You plug into your calculator, y = e^(−z²) / √(π) Then you integrate that with respect to z, from −∞ (as the lower limit of integration) to the z-score you are checking (as the upper limit of integration). This gives you the area under the standardized bell curve on the left side of a particular z-score. So, the probability that a random variable Z will be less than a given z-score, z, is: P(Zz) = 1 − P(Zz) = ∫{z→∞} e^(−Z²) / √(π) dZ If you ha vent taken integral calculus then its not expected for you to know where/how the tables are derived. And I would expect my answer to be over your head. Most calculators have statistics commands programmed in, anyway. So instead of having to integrate mathematically, you could just input your z-scores. Just know that the bell curve is drawn y = e^(−x²) / √(π) Pick some value along the x-axis and call it a z-score. Draw a vertical line from the x-axis all the way up to the curve. Everything to the left of this line/z-score and above the x-axis and below the curve... that whole area... is what you get out of a z-score table.

How Is The Rejection Region Defined And How Is That Related To The Z-Score And The P Value? When Do You Reject?

From Geography Forum:

How is the rejection region defined and how is that related to the z-score and the p value? When do you reject? Can someone please help me with this statistics question. Your help will be greatly appreciated. How is the rejection region defined and how is that related to the z-score and the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?

Answer: The "rejection region" is whatever tail(s) of the normal probability distribution (or student t-distribution, or chi-square distribution) lies beyond the critical point(s) indicated by the significance level. For instance, if you are conducting a "one-tailed test" where the alternate hypothesis alleges that some average is (let's say) HIGHER than a particular value, and you want to test it at alpha = 0.05, then the "rejection region" is the highest 5% of the sample means that would result if the ACTUAL average were exactly the particular value mentioned in the null hypothesis. You might have a historical suggestion that the mean length of all whozeewhatzis is 7.00 cm. If your alter ate hypothesis says "The mean length of all whiteheads is greater than 7.00," and you are taking a sample of 40 whiteheads to test this, then you can use the sample standard deviation and the sample size to construct a "standard error" for the sample mean. Just getting a sample mean higher than 7.00 isn't good enough; it has to be at least a few standard errors above the 7.00 cm. In the case of alpha=0.05, it would have to be at least 1.645 standard errors above the 7.00 cm. Every value larger than that lies in the "rejection region." The z-score, as you must already know, is the number of standard errors that separates the observed sample mean from the assumed null-hypothesis mean. "Examples" - my own field was planetary science research. The validity of newly-observed correlations is very often argued on the basis of some statistical significance level (probability of Type I error). Another kind of example that comes to mind is the sort of tests that have to be submitted to FDA when seeking approval for a new drug. It has to be pr oven that using the drug makes a significant difference to patients' well-being.

How Do You Calculate Percentile Using A Z Score?

From Mathematics Forum:

How do you calculate percentile using a z score? For AP Stats, I calculated the z-score which is 1.333 and I am supposed to find the percentile. (68-64)/3 was the equation with the plugged in info. Also, what value would be in the Th percentile? Thanks :)

Answer: A Z-table is used to convert percentages to Z-scores and vice verse. When I look up Z=1.33 in this Z-table (http://lilt.ilstu.edu/dasacke/eco148/ztable.htm), I get P = .9082, or 90.82%. That would be the Th percentile. You could also interpolate between Z=1.33 and Z=1.34 to get a more accurate answer. For P = 97% = 0.97, Z = 1.88 from the table.

How Do You Calculate Probability Using A Z-Score Of A Normal Distribution?

From Mathematics Forum:

How do you calculate probability using a z-score of a normal distribution? For example, mean=100 standard deviation=30 variable= less than or equal to 90 I know the z-score is 0.33 but how is probability calculated?

Answer: P(X<90) The true value for the z-scores is (X-Mean)/deviation Z=(90-100)/30 = -1/3 = -0.33 For calculate this you can use this: P(Z<-a) = 1-P(Z

How Would I Use A "Z Score" In Everyday Life?

From Mathematics Forum:

How would I use a "z score" in everyday life? How would I use a z score in everyday life? I work in a financial institution if that helps! Please explain this to me!

Answer: "z score" has several different meanings The "Altman Z score" is a predictor of bankruptcy. The formula is: Z = 0.012T1 + 0.014T2 + 0.033T3 + 0.006T4 + 0.999T5. T1 = Working Capital / Total Assets. Measures liquid assets in relation to the size of the company. T2 = Retained Earnings / Total Assets. Measures profitability that reflects the company's age and earning power. T3 = Earnings Before Interest and Taxes / Total Assets. Measures operating efficiency apart from tax and leveraging factors. It recognizes operating earnings as being important to long-term viability. T4 = Market Value of Equity / Book Value of Total Liabilities. Adds market dimension that can show up security price fluctuation as a possible red flag. T5 = Sales/ Total Assets. Standard measure for sales turnover (varies greatly from industry to industry). Over a two year period, 72% of companies scoring zero or less went bankrupt. The statistical " z score" measures deviation in a population. For example my son is 1.37 meters tall. The mean height for his age is 1.21 meters with a standard deviation of 0.08 meters. Therefore the z score for his height is (1.37-1.21)/0.08 = 2 A z score of 2 means that 98.7% of boys his age are shorter than my son and 1.3 % are taller.

How To Find Which Probability Corresponds To Which Z-Score?

From Mathematics Forum:

How to find which probability corresponds to which z-score? I'm actually making a program for my calculator (TI-84). I'm making a program for Normal Distributions, such as finding the Mean, Standard Deviation, Z-Score and Probability. Just wondering what the formula to get a z-score's probability is. I know in my class, the teacher only wants you to use some chart in the book. Thanks.

Answer: Mate, you could simply use Microsoft Excel for this. To obtain the z-score, you would have to standardize it first using the (x-m)/std deviation formula. Then, probability is obtained by doing the integration of its probability function by plugging in the correct values.

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