Given that X has a normal distribution with μ = 300 and σ = 50, i) Find the probability that X assumes a value greater than 362. ii) Find the probability that X assumes a value between 181.5 and 291. iii) Find the probability that X assumes a value less than 362.

Given that X has a normal distribution with μ = 300 and σ = 50, i) Find the probability that X assumes a value greater than 362. ii) Find the probability that X assumes a value between 181.5 and 291. iii) Find the probability that X assumes a value less than 362.

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

Related questions

Q: Suppose a population is known to be normally distributed with a mean, μ, equal to 116 and a standard…

Q: X shows a normal distribution with a mean of u=50 and a standard deviation of o=10. What standard z…

A: Standardization of a normal random variable x with mean μ and standard deviation σ is done by…

Q: find the area under the standard normal distribution curve. To the left of z = -1.45

Q: 5. Find the area under the standard normal distribution curve. A. z=0 and z=2.23 B. To the right of…

A: X~N( 0 , 1 )μ=0 , ?=1 (for standard normal distribution)Z-score =( x - μ )/?

Q: Find the area under the standard normal probability distribution between the following pairs of…

A: As per our guidelines we are suppose to answer only three sub parts . Area between Z=0.00 and 1.00

Q: In standard normal distribution, what is the area to the left of z = -2.22 ? A 0.9830 B 0.0132…

A: In standard normal distribution,what is the area to the

Q: In standard normal distribution, the area to the right of z = -1.05 is: A.0.85314 B.0.70628…

A: We have to find the area to the right of z = -1.05

Q: Let X have a normal distribution with μ= 100 and σ=20. Which two values of X is the central 70%…

A: Given information- Population mean, µ = 100 Population standard deviation, σ = 20 We have to find…

Q: Decide which of the following statements are true. A.Normal distributions are symmetric, but they…

A: Answer - Decide which of the following statements are true.

Q: Use the midpoint rule when n=4 to estimate in m2 of a pool with measurements ; 3.1, 3.6, 3.4,…

A: Given: The measurements of the pool are: 3.1, 3.6, 3.4, 2.8, 2.5, 2.4, 2.4 To find: The area of the…

Q: E. A coin is tossed 400 times. Find the probability of obtaining a) exactly 205 heads. b) less than…

Q: Cam and Denise wish to check the data from their labexperiment to see if the distribution is…

A: Box plot is an appropriate measure for checking the normality for data related to laboratory…

Q: The distribution of SAT scores is normally distributed with a μ = 500 and a σ = 100. a, What…

A: Let X be a continuous random variable of the distribution of SAT scores is normally distributed…

Q: Four items are each measured twice. The data are from normal distributions. 1 2 3 4 Sample 1 8 5 6 9…

A: As per our guidelines we can solve first three sub part of question and rest can be reposted.…

Q: In each part, find the area under the standard normal curve that lies between the specified z-score,…

A: a)Givenarea of interest between -1 and 1

Q: Use the standard normal distribution (aka z distribution where mu = 0 and sigma = 1) to determine…

A: a) The middle 90% of the data is given by, Pz1<z<z2=0.90 The critical value is obtained as,…

Q: 2) The table below provides the masses of students. Frequency 10 Mass (kg) Midpoint 40-50 50 - 60 12…

Q: Complete the statement so that it describes a normal distribution. The density curve has a…

A: Density curve which describes the normal distribution is known as normal curve. Density curve for a…

Q: 2- Bob takes on average of 50.5 hours uniformly distributed to to finish a portrait in his studio…

A: Given information- Population mean, µ = 50.5 hours Population standard deviation, σ = 10.5 hours…

Q: A sample of two hundred and fifty families showed that ninety one owned at least one car. Find an…

Q: For a standard normal distribution, find: P(z > c) = 0.2535 Find c.

A: Given that, P-value = 0.2535 Right tailed test

Q: Use Excel/Megastat to create the density probability plot of normal distribution. Take µ = 80 and σ…

A: To create a density probability plot of a normal distribution with mean (µ) 80 and standard…

Q: If the pro habi, lita given by: function of random variable ir f Cx) = %3D Sechx 9. find the mean b.…

A: The probability function of random variable is given by : fx=1sec hx , 1≤x≤2 a) Here we have to find…

Q: Find the z-scores that are exceeded by the following proportions of the area under the normal…

Q: Suppose a population is known to be normally distributed with a mean, μ, equal to 116 and a standard…

A: Given X is normal Distributed with mean µ = 116.0 and standard deviation σ = 14.0 now will using…

Q: The area under the normal distribution is equal to which rule?

A: Area under normal curve lie between μ- 3σ and μ+3σ

Q: What is the approximate shaded area under the normal curve shown below? - 20 -lo A) 95% B) 84.5% C)…

A: The empirical rule states that if a distribution is unimodal and symmetric i.e. more or less…

Q: In a normal distribution, approximately what percentage of the data falls within one standard…

A: Step 1: Define how to use the 68-95-99.7/Empirical RuleAccording to the 68-95-99.7/Empirical…

Q: In a normal distribution, about what proportion of cases falls within +/- 1 standard deviation from…

A: From the provided information,It is asked what proportion of cases falls within +/- 1 standard…

Q: he thickness of ice at various locations on a frozen lake (in inches) can be represented by the…

A: X~N(4.5, 0.252) a) We have to calculate a and b such that, P(a<x<b) =0.68…

Q: A forest ranger has data on the heights of a large growthof young pine trees. The mean height is 3.2…

A: Denote the random variable X as height of trees. Here X follows normal distribution with µ= 3.2, σ=…

Q: II. Find the area under the standard normal distribution curve. Draw the figure and represent the…

Q: Examine the image below and then answer all parts of the question under it. Enter your answers as…

A: a) There are 4 yellow objects in 10 objects.So, P(yellow)=410=0.4b) There are 3 hearts in the 10…

Q: Let Z be the standard normal variable. Find the values of z if z satisfies the following: P(Z < -z)…

A: From the provided information,Let Z be the standard normal variable.P(Z < -z) = 0.8365

Q: Let Z be the standard normal variable. Find the values of z if z satisfies the following: P(Z < z)…

A: Let Z be the standard normal variableP(Z<z)=0.9251

Q: For a t distribution with 16 degrees of freedom, find the area, or probability, in each region. a.…

A: The t table provides the area to the right of the t values corresponding to the degrees of…

Q: Assume that x has a normal distribution with the specified mean and standard deviation. Find the…

A: Mean = 107 Standard deviation = 14

Q: assume that x has a normal distribution with the specified mean and standard deviation. Find the…

A: The standard normal distribution is the improvisation of normal distribution. If we substitute…

Q: Given a normal distribution with u = 35 and o = 8, find: a) the normal curve area to the right of x…

A: Given Data Population Mean,μ = 35.0 Population Standard Deviation,σ = 8.0 follows…

Q: The method of tree-ring dating gave the following years A.D. for an archaeological excavation site.…

A: Given data, 1236 ,1180 ,1229, 1208 ,1268 ,1316, 1275, 1317 ,1275 n=9

Q: Assume z follows a standard normal distribution: a.P(X=2) b.P(X=2) d.P(2 < X < 4)

A: z follows a standard normal distribution: from z distribution table, a. P(X =2) = P(0<x<Z) =…

Q: Let Z be the standard normal variable. Find the values of z if z satisfies the following: P(Z > z)…

A: P(Z > z) = 0.3336

Q: Suppose a population is known to be normally distributed with a mean, μ, equal to 116 and a standard…

Question

Given that X has a normal distribution with μ = 300 and σ = 50,
i) Find the probability that X assumes a value greater than 362.
ii) Find the probability that X assumes a value between 181.5 and 291.
iii) Find the probability that X assumes a value less than 362.
iv) Find the value of x such that it has 42.8% of the area to the left.

Note: Tabulated values are at the end

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

If z is a standard normal variable, find P (z > 0.97). 0.1922 0.1660 0.8340 0.1685
II. Find the area under the standard normal distribution curve. Draw the figure and represent the area a) Between z = 0 and z = 1.49 Solution: b) Between z 0.46 and z = 2.57 Solution:
Let Z be the standard normal variable. Find the values of z if z satisfies the following: P(-z < Z < z) = 0.8502 A) 1.81 B) 0.24 C) 1.44 D) -0.71 E) 0.79
Let X follow the normal distribution with μ = 100 and σ = 10. Then P(X < 120) is closest to: a. 0.023 b. 0.046 c. 0.430 d. 0.853 e. 0.977
A random variable x is best described by a normal distribution with μ = 30 and o =10. Find the z-score that corresponds to the value x = 35. A) 5 B) 0.5 C) 1/6 D) 3.5
What is the area of -0.45 in the standard normal distribution? A.) 1 B.) 0.5 C.) 0.6736 D.) 0.3264 E.)0 F.) None of the above, as it depends on the situation
The IQ of a person follows a normal distribution and has a mean of 100 and a standard deviation of 15. What percentage of the people have IQ scores between 70 and 130? A) 95% B) 50% C) 2.5% D) 68%
Find the area under the standard normal probability distribution between the following pairs of z-scores. a. z = 0 and z = 1.00 b. z = 0 and z = 2.00 c. z = 0 and z=3.00 d. z = 0 and z=0.46 e. z = -1.00 and z = 0 f. z = -2.00 and z=0 g.z= -1.67 and z=0 h. z = -0.46 and z=0 a. The area under the standard normal probability distribution is 0.314 (Round to three decimal places as needed.) b. The area under the standard normal probability distribution is 0.477 (Round to three decimal places as needed.) c. The area under the standard normal probability distribution is 0.499 (Round to three decimal places as needed.) d. The area under the standard normal probability distribution is (Round to three decimal places as needed.) e. The area under the standard normal probability distribution is (Round to three decimal places as needed.) f. The area under the standard normal probability distribution is (Round to three decimal places as needed.) g. The area under the standard normal probability…
Find the Z scores for which 90% of the distributions area lies between -z and z 1) -1.96 ,1.96 2) -0.99 ,0.99 3) -1.645, 1.645 4) -2.33, 2.33 select the correct answer
Select all statements that are true for density curves. The curve is symmetric and single-peaked. The curve is on or above the horizontal axis. The proportion of data values between two numbers ?a and ?b is the area under the curve between ?a and ?b. The total area under the curve is 1. The curve satisfies the 68-95-99.7% rule.
Solve for C) answer b was wrong