The stochastic variable X is the proportion of correct answers (measured in percent) on theexam in mathematics for a random engineering student. We assume that X is normallydistributed with the expected value = 57.9% and the standard deviation o = 14.0%, ieX~ N(57.9; 14.0).(a) Find the probability that a randomly selected student has more than 60% correctly onthe exam in mathematics, ie P(X > 60).(b) Consider 81 students from the same cohort. What is the probability that at least 30 ofthem get over 60% correctly on the math exam? We assume that the students' results areindependent of each other.(c) Consider 81 students from the same cohort. Let X be the average value of the result(measured in percent) on the exam in mathematics for 81 students. What is the probabilitythat X is above 60%?

Normal and binomial pdf has utilized

Answered: The stochastic variable X is the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Today, the waves are crashing onto the beach every 4.4 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.4 seconds. Round to 4 decimal places where possible. The probability that the wave will crash onto the beach between 1.2 and 2.1 seconds after the person arrives is P(1.2 < x < 2.1) = The probability that it will take longer than 3.28 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.28) = Suppose that the person has already been standing at the shoreline for 0.7 seconds without a wave crashing in. Find the probability that it will take between 3 and 3.7 seconds for the wave to crash onto the shoreline. 62% of the time a person will wait at least how long before the wave crashes in? seconds. Find the minimum for the upper quartile. seconds. Hint:
Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean ? = 45 and standard deviation ? = 11. Find the following probabilities. (Round your answers to four decimal places.) (a) x is less than 60(b) x is greater than 16(c) x is between 16 and 60(d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000 miles of driving) of cars of a particular model varies Normally with mean 90 mg/mi and standard deviation of 4 mg/mi. A company has 25 cars of this model in its fleet. Find the level L such that the probability that the average NOX + NMOG level bar x for the fleet greater than L is only 0.03? Round final answer to three decimals.
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,…
A pizza company advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas. Suppose that the amount of cheese on a randomly selected medium pizza is normally distributed with a mean value of 0.5 pounds and a standard deviation of 0.005 pounds. (Let y = the amount of cheese on a medium pizza. Round the answers to three decimal places.) (a) What is the probability that the amount of cheese on a medium pizza is between 0.505 and 0.510 pounds?P(0.505 ≤ y ≤ 0.510) = (b) What is the probability that the amount of cheese on a medium pizza exceeds the mean value by more than 2 standard deviations?P(y > ? + 2?) = (c) What is the probability that four randomly selected medium pizzas all have at least 0.495 pounds of cheese?
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr
Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean ? = 35 and standard deviation ? = 11. Find the following probabilities. (Round your answers to four decimal places.) (a) x is less than 60 (b) x is greater than 16 (c) x is between 16 and 60 (d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)
Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean μ = 39 and standard deviation σ = 13. Find the following probabilities. (Round your answers to four decimal places.) (a) x is less than 60(b) x is greater than 16(c) x is between 16 and 60(d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)
'Melanoma' is a form of skin cancer and each year 17% of the patients who suffer from the disease die. A random sample of 10,000 melanoma patients is formed at the start of a year. Let Y denote the number of patients in this sample who will die during the year? (a) What is the expected value of Y? That is, compute E(Y). Answer: [Select] (b) What is the variance of Y? That is, compute var(Y). Answer: [Select] (c) What is the probability that Y exceeds 1,800? That is, compute P(Y> 1,800). Answer: [Select]
Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean ? = 35 and standard deviation ? = 10. Find the following probabilities. (Round your answers to four decimal places.) (a) x is less than 60 (b) x is greater than 16 (c) x is between 16 and 60 (d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.4 and ß = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.74310 0.74310 0.12183 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 6032 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) hr
Fawns between 1 and 5 months old in Mesa Verde National Park have a body weight that is approximately normally distributed 25.36 kg and standard deviation q = 4.72 kg. Let x be the weight of a fawn in kg. What is the probability that for a fawn chosen at random: with mean u - (a) x is less than 28.88 kg? (b) x is greater than 17.34 kg? (c) x lies between 29.04 and 33.6 kg? -

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