Given the normally distributed random variable X with mean 100 and standard deviation 15, find the numerical value of k such that: (a) PðX kÞ 1⁄4 :0094 (b) PðX ! kÞ 1⁄4 :1093 (c) Pð100 X kÞ 1⁄4 :4778

Given the normally distributed random variable X with mean 100 and standard deviation 15, find the numerical value of k such that: (a) PðX kÞ 1⁄4 :0094 (b) PðX ! kÞ 1⁄4 :1093 (c) Pð100 X kÞ 1⁄4 :4778

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

See similar textbooks

Related questions

Q: A random sample of n = 25 observations is drawn from a population with mean 10 and standard…

A: Given, A random sample of n = 25 observations is drawn from a population with mean 10 and standard…

Q: 5. Given the normally distributed random variable X with mean 100 and standard deviation 15, find…

Q: The strength of a weld is determined by the formula X = O + 3N + 5C where X is the strength, and O,…

A: Given,μo = 0.1665μN = 0.0455μc = 0.0346σo = 0.0340σN = 0.011σc = 0.0131X = 0 + 3N+5Ca) ∈(X)…

Q: Given that z is a standard normal random variable, find z for each situation. a. The area to the…

A: Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.2119 to the left of…

Q: Given the normally distributed random variable X with mean 100 and standard deviation 15, find the…

Q: An office has four copying machines, and the random variable X measures how many of them are in use…

Q: If two loads are applied to a cantilever beam as shown in the figure below, the bending moment at 0…

A: Given : Bending moment : a1x1+a2x2 x1 and x2 are indep. . μ(x1)=4 , μ(x2)=6 σ(x1)=0.7 , σ(x2)=1.3…

Q: Given that z is a standard normal random variable, find for each situation (to 2 decimals). A) The…

A: Note :“Since you have posted a question with multiple sub-parts, we will solve first three subparts…

Q: discrete random variable X has the following probability distribution: Value of X 1 2 3 4 5 6…

A: Given that Probability distribution table X 1 2 3 4 5 6 P(X) 0.30 0.20 0.15 0.15 0.10 0.10…

Q: Given the normally distributed random variable x with μ =25 and P(x ≤ 10) = .0778, find σ.

A: Given,mean(μ)=25P(X≤10)=0.0778

Q: Given a normal random variable X with mean 15 and variance 16, suppose you take a random sample of…

A: Given a normal random variable X with mean μ=15 and variance σ2=16 with unknown sample size n. And…

Q: If ZZ is a random variable from a standard normal distribution and if P(Z<b)=0.6P(Z<b)=0.6, then…

Q: Given a random variable X that is distributed Normally with a mean of 94 and a standard deviation of…

Q: The amount of gasoline in gallons sold by three different gas stations during one day is given by…

A: Given that E(X1)= 600, E(X2)= 800, E(X3)= 850 And σ1= 55, σ2= 75, σ3= 100 Prices , a= 3.10, b= 3.20…

Q: If X is a normally distributed random variable with mean 97 and standard deviation 10, find x2 such…

Q: Let z be a normal random variable with mean 0 and standard deviation 1. The 50th percentile of z is…

A: Given that, Z be a normal random variable with mean 0 and standard deviation 1.

Q: For a standard normal random variable Z, P(|Z|<1.30) is closest to: A 0.1936 b 0.4032 c…

A: Option (c) is correct

Q: Given a Normally distributed population with a mean of 175 and a standard deviation of 40 find x…

Q: P(x) 0.645 1. 0.297 0.052 0.005 0.001 0.000 2345

A: We have to use following formulae , Standard deviation : σ = ∑( x - μ)2p(x) Where , μ is mean μ =…

Q: Let z be a normal random variable with mean 0 and standard deviation 1. Which of these most closely…

A: Draw the normal curve.

Q: Let X 1 be a normal random variable with mean 2 and variance 3 and let X 2 be a normal random…

Q: Let X be a random variable with P(X = 1) = 0.2, P(X = 2) = 0.3, and P(X = 3) = 0.5. What is the…

A: Given information: The random variable X has the following probability distribution: X P(X=x) 1…

Q: Compute the mean (ux) variance (a³x) and standard deviation (ax) of each sampling distribution. 1.…

A: As per our company guidelines we are suppose to answer only one question1)Given data is x 1 2 3…

Q: Let X and Y be two independent random variables, each of which follow a normal distribution with the…

A: Given information: X~N+μ, σ Y~N-μ, σ

Q: Given independent random variables X and Y with mean and standard deviations as shown, Mean St.…

A: A) σx=2σy=2σx+y=σx2+σy2=4+4=2.8284 B) μx-y=μx-μy=9σx-y=σx2+σy2=4+4=2.8284

Q: 2. Suppose a random variable X is normally distributed with a mean of 5 and a standard deviation of…

A: The normal distribution is the most useful theoretical distribution for continuous variable. For…

Q: Given that z is a standard normal random variable, find c>0 such that P(−c<z<c)=0.8968

Q: Given that z is a standard normal random variable, find z for each situation (to 2 decimals). a. The…

Q: Use the z-table (attached to this test), calculator, or computer software to find the following:

A: Given: The random variable X approximately follows a normal distribution with mean (µ) is 0.01 and…

Q: A random variable X has P( 1.2 < X< 18.8 ) 2 15/16. Use Chebyshev's Theorem to find the standard…

A: According to chebyshev's theorem, the proportion of a distribution which will lie within k standard…

Q: Given a normally distributed random variable with mean 18 and standard deviation 2.5, the value of k…

A: The given values are, μ=18,σ=2.5 The value of k such that P(x<k) = 0.3192 is,

Q: Classify the following random variables as discrete or continuous. 1. X-the number of mobile phonce…

A: The discrete random variable can take countable number of distinct values. The continuous random…

Q: Consider a standard normal random variable with mean=1.2 and standard deviation=0.7, find the…

Q: Given a normally distributed random variable with a mean of 196 and a standard deviation of 20, find…

A: In this context, it is given that X follows normal distribution with a mean of 196 and a standard…

Q: Given independent random variables with means and standard deviations as shown, find the mean and…

Q: Given z is the standard normal random variable, find c > 0 such that P(-c<z < c) = 0.135

A: given z is the standard normal random variable. z~N(0,1) find c=? s.t. P(-c<z<c)=0.135 ,…

Q: b) If W is a chi-square random variable with 16 degrees of freedom and Y is a standard normal…

A: A continuous random variable Z is said to follow Standard Normal distribution if its probability…

Q: The parameter of a Poisson random variable, X, is λ=5.9. a. Determine P(X=6), P(4≤X≤7), and…

A: Given Information: Parameter of Poisson random variable X is λ=5.9

Q: random variable X is normal with mean 2 and standard deviation 2, then what is P(x2 - 4x < 1). 3

Q: q14- If the random variable X is normally distributed with a mean of 75 and a standard deviation of…

A: Option D is correct.

Q: X is a discrete random variable with the following PMF: P(X = -9.2) = 0.25 P(X = -2.5) = 0.25 P(X =…

Q: et x be a binomial random variable with n = 20 and p = 28 / 100. a-)Calculate the mean, variance…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: A random sample of size 20 from a normal population gives the sample standard deviatio of 6. Test…

A: Any assumption about the parameter or probability function is known as hypothesis testing. For the…

Q: Suppose X is a random variable distributed with mean u and standard deviation ơ > O. If the random…

Q: Given that z is a standard normal random variable, find z for each situation.a. The area to the left…

Q: Given that z is a standard normal random variable, find z for each situation (to 2 decimals). A.…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Given that z is a standard normal random variable, find z for each situation (to 2 decimals). A)…

Q: Given a normally distributed random variable X with a mean of 196 and a standard deviation of 20,…

A: Given mean = 196 Standard deviation = 20

Q: For a standard normal random variable Z, what is the value of k such that P(Z>k)=0.8790?

Question

Given the normally distributed random variable X with mean 100 and standard deviation 15, find the numerical value of k such that:

(a) PðX kÞ 1⁄4 :0094
(b) PðX ! kÞ 1⁄4 :1093
(c) Pð100 X kÞ 1⁄4 :4778
(d) Pðk0 X kÞ 1⁄4 :9660, where k0 and k are equidistant from m

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution