Compute probabilities.Recall the following definitions from section 6.4 of the text.The area under the normal curve from x = a to x = b with given mean and standard deviation is the probability that x assumes a valuebetween x = a and x = b. If we are using Table IV in Appendix C, we need to standardize the random variable x using the formula z = (x -H)/o, before using the table.Alternatively, you may use a graphing calculator to obtain more accurate calculations without standardizing the random variable x.For example, using a TI83 plus we calculate the area under the normal curve from x = a to x = b by using thenormalcdf(a,b,u,o)where u is the mean and o is the standard deviation of the normal distribution. We use 1E99 for o and -1E99 for -o, if needed.Chapter 06, Section 6.2, Intelligent Tutoring Problem 023Let x be a continuous random variable that is normally distributed with a mean of 27 and a standard deviation of 7.Round your answers to two decimal places.(a) Standardize the variable value x = 31.7.Z =i(b) Standardize the variable value x = 62.0.Z =i

a) Consider that the mean and standard deviation of a random variable x are µ and σ, respectively.…

Answered: Let x be a continuous random variable…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 20 . Find the probability that a randomly selected adult has an IQ less than 95 a. Find the z-score: z = nothing (round to 2 decimal places) b. Find the probability: nothing (use 4 decimal places)
A survey collected data from a random sample of 121 people living in Jade city. The sample average of the distance people travel to reach their workplaces (Y) is 23.28 km and the standard deviation (sy) is 7.48 km. The standard error of the sample average of the distance people travel to reach their workplaces is 68 km. (Round your answer to two decimal places.) Let μy denote the mean of the distance all the people in Jade city travel to reach their workplaces. The p-value of the test Ho: #y #22 km vs. H₁: Hy #22 km is (Round your answer to two decimal places.)
A population has mean u=30 and standard deviation o=7. (A) Find the z-score for a population value of 9. (B) Find the z-score for a population value of 51. (C) What number has a z-score of -2.3
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 46 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.80 ml/kg for the distribution of blood plasma. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.90 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) ________ male firefighters
Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.78. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = s = (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.78? Use ? = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. H0: ? < 4.78; H1: ? = 4.78H0: ? = 4.78; H1: ? ≠ 4.78 H0: ? = 4.78; H1: ? < 4.78H0: ? = 4.78; H1: ? > 4.78H0: ? > 4.78; H1: ? = 4.78 (b) What sampling…
A persons blood glucose level and diabetes are closely related XB a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Supposed to after a 12 hour fast the random variable X will have a distribution that is approximately normal with mean of u=87 and a standard deviation of O=25. Note: after 50 years of age both the mean and Standard deviation tends to increase for an adult under 50 after 12 hour fast find the following probabilities A) X is more than 60 B) X is less than 60 C) X is between 60 and 110 D) X is greater than 125 (borderline diabetes starts at 125)
The variable W represents the weight of potatoes buns sold at the bakery. This variable is normally distributed with mean 90 g and standard deviation 6 g. (a) (i) Explain the meaning of S6 . (ii) Find the mean and standard deviation of S6 . (ii) Hence, Calculate P ( S6 2 560 g).
Let x be a random variable that represents the pH of arterial plasma (l.e., acidity of the blood). For healthy adults, the mean of the x distribution is = 7.4.t A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.8 with sample standard deviations = 3.3. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Hg: u + 7.4; H,: = 7.4 O Hg: H = 7.4; H,: H > 7.4 O H,: H = 7.4; H,i 7.4; H,: H = 7.4 O H: = 7.4; H,: H# 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large a is known. O The standard normal, since the sample size is large and a is known. O The standard normal,…
Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (1) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x=| S= (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ο Hg: μ= 4.64; H1: μ 4.64 Ο Ηρ: μ> 4.64; H1: μ = 4.64 Ho: u = 4.64; H1: u * 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O…
+ I/ * 00 A company manufactures light bulbs. The company wants the bulbs to have a mean life span of 997 hours. This average is maintained by periodically testing random samples of 16 light bulbs. If the t-value falls between -th an and t, go then the company will be satisfied that it is manufacturing acceptable light bulbs. For a random sample, the mean life span of the sample is 1002 hours and the standard deviation is 29 hours. Assume that life spans are approximately normally distributed. Is the company making acceptable light bulbs? Explain. and to 90 The company making acceptable light bulbs because the t-value for the sample is t= (Round to two decimal places as needed.) Get more help- Clear all Check answer 3:44 PM 64°F Sunny A 11/23/2021 PrtSc F5. F10 F11 F12 4. 5. 9. 6. K. B. M.
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 42 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 8.00 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limitupper limitmargin of error (b) What conditions are necessary for your calculations? (Select all that apply.) the distribution of volumes is uniform? is knownn is largethe distribution of volumes is normal? is unknown (c) Interpret your results in the context of this problem. We are 99% confident that the true average blood…
Determine the standard deviation of the random variable, B(600,0.4).

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Let x be a continuous random variable that is normally distributed with a mean of 27 and a standard deviation of 7. Round your answers to two decimal places. (a) Standardize the variable value x = 31.7. i (b) Standardize the variable value x = 62.0. i