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...

See similar textbooks

Similar questions

Let X be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood). The distribution of X for a healthy person is normally distributed with men u = 85 and standard deviation o = 25. A person suffers from severe excess in insulin would have a lower level of glucose. A blood test with result of X < 40 would be used as an indicator that medication is needed. (a) What is the probability that a healthy person will be suggested with medication after a single test? (b) A doctor uses the average result of 2 tests for diagnosis, that is X. The second test will be conducted one week after the first test, so that the two test results are independent. For many healthy persons, each has finished two tests, find the expectation and standard error of the distribution of X. (c) The doctor suggests medication will be given only when the average level of glucoses in the 2 blood tests is less than 40, that is X < 40, so to reduce the chance of…
Consider a random variable X that follows a normal distribution with a mean (μ) of 50 and a standard deviation (σ) of 5. Calculate the probability that X is less than 40.
If XX represents a random variable coming from a normal distribution and P(X<10.2)=0.22P(X<10.2)=0.22, then P(X>10.2)=0.78P(X>10.2)=0.78. true or false
Suppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random variable with CDF F(x) = 1 − e-x/3 x ≥ 0 What is the probability that the battery lasts between 12 to 15 months?
Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution. X 0 1 2 3 4 5 P(x) 0.05 0.25 0.30 0.25 0.10 0.05 Send data to Excel
(d)
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]

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS