MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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If an entire population with μ = 60 and s = 8 is transformed into z-scores, then the distribution of z-scores will have a
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- (a) The population 3, 4, 9, 14, and 20 has a mean of 10 and a standard deviation of 6.356. The z-scores for each of the five data values are z3 ≈ −1.101, z4 ≈ −0.944, z9 ≈ −0.157, z14 ≈ 0.629, and z20 ≈ 1.573. Find the mean and the standard deviation of these z-scores. mean standard deviation (b) The population 2, 6, 12, 17, 22, and 25 has a mean of 14 and a standard deviation of 8.226. The z-scores for each of the six data values are z2 ≈ −1.459, z6 ≈ −0.973, z12 ≈ −0.243, z17 ≈ 0.365, z22 ≈ 0.973, and z25 ≈ 1.337. Find the mean and the standard deviation of these z-scores. mean standard deviation (c) Use the results of part (a) and part (b) to make a conjecture about the mean and standard deviation of the z-scores for any set of data. The mean of the z-scores is always 1, and their standard deviation is 0. The mean of the z-scores is always 1 more than the standard deviation. The mean and standard deviation of z-scores are never the same.…arrow_forwardSuppose the scores of students on an exam are Normally distributed with a mean of 522 and a standard deviation of 83. Then approximately 99.7% of the exam scores lie between the numbers such that the mean is halfway between these two integers. and ☐arrow_forwardA person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 86 and standard deviation o = 23. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) USE SALT (a) x is more than 60 1292 (b) x is less than 110 0.9236 X (c) x is between 60 and 110 0.7526 (d) x is greater than 125 (borderline diabetes starts at 125) 6.3arrow_forward
- Suppose X has a normal distribution with mean 80 and standard deviation 5. How many standard deviations above or below the mean is 70? None of the other choices is correct 10 standard deviations below the mean O2 standard deviations above the mean 2 standard deviations below the meanarrow_forwardCalculate z scores for a population with a mean of 1179 and a standard deviation of 164 for each raw scores: If X = 1000 What is Z =? If X= 1,184 what is Z =?arrow_forwardThe mean score on a driving exam for a group of driver’s education students is 76 points, with a standard deviation of 6 points. Apply chebychev’s theorem to the data using K=2. Interpret, At least ___% of the exam score falls between ___and ____arrow_forward
- The brain volumes (cm³) of 20 brains have a mean of 1093.1 cm³ and a standard deviation of 120.6 cm³. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1284.3 cm³ be significantly high? Significantly low values are cm³ or lower. (Type an integer or a decimal. Do not round.) Significantly high values are 0cm³ (Type an integer or a decimal. Do not round.) Is 1284.3 cm³ significantly high? cm³ or higher. OA. Yes, because it is above the upper limit separating value. OB. No, because it is between the limits separating values. O C. No, because it is above the upper limit separating value. O D. Yes, because it is between the limits separating values. OE. Yes, because it is below the lower limit separating value. OF. No, because it is below the lower limit separating value.arrow_forwardIn the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?arrow_forwardThe brain volumes (cm³) of 20 brains have a mean of 1113.7 cm³ and a standard deviation of 128.9 cm³. Use the give standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1361.5 cm³ be significantly high? 3 Significantly low values are cm³ or lower. (Type an integer or a decimal. Do not round.)arrow_forward
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