Chapter 4 1. Assume that Z has a standard normal distribution. Use Table given to you determine the following (a) P(Z <=)=0.9 (b) P(-z
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- IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = 1Q of an individual. (a) Find the z-score for an IQ of 97, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 97. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z- Score. Use your z-score from part (a), rounded to one decimal place). Shade: Left of a value Click and drag the arrows to adjust the values. -1 3 4 -1.5 (d) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. (e) Sketch the graph, and write the probability statement. BIUX, x' C 次四 Edit. Insert - Formats - Σ ΣΗSuppose 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 meanDetermine the area under the standard normal curve that lies to the right of (a) Z= - 0.27, (b) Z= - 0.68, (c) Z = 0.11, and (d) Z= – 1.16. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). Standard normal distribution kable (page 2) (a) The area to the right of Z= - 0.27 is (Round to four decimal places as needed.) Area Standard Nornal Distribution 0.05 0.00 0.01 0.02 0.03 0.04 0.06 0.07 0.08 0.09 0.5000 0.5398 0.5793 0.6179 0.6554 0.5040 0.5438 0.5832 0.5080 0.5478 0.5871 0.6255 0.6628 05120 0.5517 0.5910 0.6293 0.6664 0.5160 0.5557 0.5948 0.5199 0.5596 0.5987 0.5239 0.5636 0.6026 0.6406 0.6772 0.5279 0.5675 0.6064 0.6443 0.6808 0.5319 0.5714 0.6103 0.5359 0.5753 0.6141 0.0 0.1 0.2 0.3 0.4 0.6217 0.6591 0.6331 0.6700 0.6368 0.6736 0.6480 0.6844 0.6517 0.6879 0.7190 0.7517 0.7823 0.7224 0.5 0.6 0.7 0.6915 0.7257 0.7580 0.7881 0.8159 0.6950 0.7291 0.7611 0.7910 0.8186 0.6985 0.7324 0.7642 0.7019…
- Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 4.3 and standard deviation ? = 0.5. (a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.) < z(b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.)z < (c) Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.) < z < (d) Convert the z interval, z < −1.44, to an x interval. (Round your answer to one decimal place.)x < (e) Convert the z interval, 1.28 < z, to an x interval. (Round your answer to one decimal place.) < x(f) Convert the z interval, −2.25 < z < −1.00, to an x interval. (Round your answers to one decimal place.) < x <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)
- Don't know how to solveAssume that X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the following: a. P(Z < 13) b. P(Z > 9) c. P(6 < X < 14)Assume a variable is normally distributed with a mean of 30 and standard deviation of 6. P(x>32) = Round to three decimal places. N
- Find P(27 < X < 32) if X is normally distributed with mean 24 and standard deviation 5.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…David and Patrick are playing baseball for the Cafe Tropical team. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. If X = distance in feet for a fly ball, then X ~ N ( , ) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled less than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability. P = Find the 80th percentile of the distribution of fly balls. 80th Percentile: feet