Answered: if X is normally distributed withe mean…

Math

Probability

if X is normally distributed withe mean 10 and standard deviation 2, what is the probability that X is less than 5?

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 we have a set of measures that is normally distributed with mean O and standard deviation 1.…

A: First quartile: There are 25% of observations less than the first quartile and 75% of the…

Q: Suppose that, in fact, the total cholesterol level of all men aged 20–34 follows the Normal…

Q: The life time of a particular steel plate used in constructions has a normal distribution with a…

A: we have given that, the construction normally distributed with mean (mu)= 80 and standard deviation…

Q: If a distribution is normal, then it is not possible to randomly select a value that is more than 4…

A: Given : We have given normal distribution .

Q: Suppose x has a distribution with mean =30 and standard deviation 28 P(30<x<32)=

A: Given, mean μ=30 standard deviation, σ = 28 X ~ N(μ, σ)

Q: is a normal random variable with mean 20 and stadard deviation 50. Find the probability that 15

A: Answer the population mean = 20The population standard deviation = 50Using formula:P [A<Z<B] =…

Q: Suppose a population of GRE scores has mu = 1000 and standard deviation = 100. Assuming normality,…

A: Given Data Population Mean,μ = 1000.0 Population Standard Deviation,σ = 100.0…

Q: Suppose one value is selected from a uniform distribution with a = 0 and b = 11. What is the…

A: Given: X~U(0,11) a=0 b=11

Q: Given a random variable X that follows a normal distribution with mean = 100 and standard deviation…

Q: If babies have birth weights that are approximately normally distributed with mean 3.3kg and a…

A: Given : μ=3.3 kgσ=0.55 kgX~N(μ=3.3,σ2=(0.55)2) We want to find, P(X > 5) = ?

Q: A random variable is normally distributed with mean 10 and standard deviation of 2. What is…

A: Normal distribution is a continuous distribution which has many real life applications. The normal…

Q: Suppose IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What…

Q: Suppose the weight of hummingbirds are distributed normally with a mean of 25 oz and a standard…

A: Obtain the probability that a randomly selected hummingbird weighs more than 28oz. The probability…

Q: Assuming you obtained a random sample of blood glucose levels from 32 individuals from a population…

A: Central Limit Theorem for mean:If a random sample of size n is taken from a population having mean µ…

Q: The average time required to complete an accounting test has been determined to be 55 minutes with a…

A: We assume the data is normally distributed.

Q: What is the probability a randomly selected student's score is between 402 and 509.92?

A: It is given that Mean, μ = 438 Standard deviation, σ = 58 Z-Score, Z = ( X - μ )/σ

Q: What is the z-score of x = 11, if it is 2.5 standard deviations to the left of the mean?

Q: Suppose that heights of 10-year-old boys in the US vary according to a normal distribution with mean…

Q: Suppose that X is normally distributed with mean 120 and standard deviation 16 A. What is the…

Q: A random variable X is normally distributed with mean = 80 and standard deviation = 4.5. What is the…

A: What is the probability that X is at least 81.6 ?

Q: What is the probabilities associated with the normal distribution of a P(z >= .23) =

A: Z score is given z = 0.23 Using Excel formula =NOMSDIST(0.23) or Z table we find the probabilities…

Q: Assume the random variable X is normally distributed with a mean of 50 and a standard deviation of…

Q: What is the z-score of x = 9, if it is 0.133 standard deviations to the left of the mean?

A: Given X=9,

Q: 11. What is the z score for an IQ score of 110? 12. What is the probability of randomly selecting…

Q: A random variable X is normally distributed with mean = 80 and standard deviation = 4.5. What is the…

A: The random variable X follows normal distribution. The population mean is 80. The population…

Q: In a certain factory average length of products is 26 cm and standard deviation is 6 cm.…

A: Given Information: Distribution of lengths of products in a certain factory is assumed to be normal.…

Q: Suppose that x is a normally distributed with mean 36 and standard deviation 18, find the given…

A: Answer: From the given data, Mean (μ) = 36 Standard deviation(σ) = 18 X follows normal distribution,

Q: Find the probability of z greater than 0.5 if mean is 0 and standard deviation is 1.

A: Given, Mean=0 S.D=1 P(z>0.5)=?

Q: The scores on a certain test are normally distributed with a mean score of 65 and a standard…

A: The random variable score follows normal distribution. The population mean is 65. The population…

Q: The time for a student to commute from home to a university campus is Normally distributed with a…

A: It is given that the mean is 25 minutes and the standard deviation is 10 minutes.

Q: iven a normal distribution (X) with mean = 100 and standard deviation () = 10, what is the…

A: Given data,μ=100σ=10P(X>101)=?

Q: The plasma cholesterol level (mg/dL) for patients who have not been diagnosed with heart disease and…

A: We have to find out given probability..

Q: the annual precipitation has normal distribution with a mean of 109 and standard deviation of 10.…

Q: If X is a normally distributed random variable with a mean of 235 Find the standard deviation given…

Q: Suppose that x is a normally distributed with mean 32 and standard deviation 16, find the given…

A: Answer: From the given data, X is a normal random variable with Mean μ = 32 Standard deviation σ =…

Q: Suppose X is a normal random variable with mean µ = 70 inches. If P(X > 79) = 0.025 what is the…

A: It is given that the random variable X follows normal distribution with mean µ as 70 and standard…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

if X is normally distributed withe mean 10 and standard deviation 2, what is the probability that X is less than 5?

Video Video

Expert Solution

Step 1

Given,

$\begin{matrix} P (x, 5) = P (\frac{X - μ}{σ} < \frac{5 - 10}{2}) \\ = P (z < - 2.5) \\ = 0.00621 \{U \sin g E x c e l S y n t a x [N O R M . S . D I S T (- 2.5, T R U E)]\} \end{matrix}$ X is normally distributed with mean µ=10 and standard deviation σ=2.

i.e. X~N (10,2)

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

If the probability that the random variable Z with a standard normal distribution is between the -k and k values is 0.90, which is ?
if one score is randomly selected from a normal distribution with a population mean of 22 and a standard deviation of 16, what is the probability of obtaining a score between X=30 and X=22?
Suppose steel wires have the tensile strength represented by a normal distribution with mean value equal to 5000N and standard deviation equal to 150N. Knowing that these wires will be used in the manufacture of a steel cable to be mounted on the boom of a crane, what should be the number of wires to be used in the manufacture of this cable so that the probability of the cable breaking with a load less than 50,000N is 2%?What would be the safety factor associated with this probability of failure?Suppose the resistance of the cable is expressed by the sum of the resistance of the wires that make it up.
What is the probability that 46 cars chosen at random will have a mean load weight x of less than 85.5 tons of coal if the mean is 86 and standard deviation 1.4
X is a normally distributed random variable with mean 22 and standard deviation 7. What is the probability that X is between 1 and 43?
If X is a normal random variable with mean 20 and standard deviation 50. Find the probability that 15 < X < 45.
The mean production in a certain factory is 10 products per hour with a standard deviation of 1.5 products per hour. What is the probability of finishing more than 12 products per hour?
Consider a random variable X that follows a normal distribution with mean 100 and standard deviation 20. What is the probability that X is less than 140?
Suppose that the number of customers who enter a supermarket each hour is normally distributed with a mean of 650 and a standard deviation of 230. The supermarket is open 15 hours per day. What is the probability that the total number of customers who enter the supermarket in one day is greater than 10400? (Hint: Calculate the average hourly number of customers necessary to exceed 10400 in one 15-hour day.) Probability =
If a random member (x) is selected from a normal distribution having a mean of 80 and standard deviation of 5, what is the probability that the value of x lies between 78 and 83? Show your formula etc along with your answer.
The test score of a physics class with 160 students is distributed normally with a mean of 75 and standard deviation of 7. what percentage of the class has a test score between 68 and 82 Approximately how many students have a test score between 61 and 89? What is the probability that a student chosen at random has a test score between 54 and 75? Approximately how many students have a test score greater than or equal 96?