The random variable X follows a normal distribution ?(20, 102).Find P(10 < ? < 35),

Dillard 2021-01-15 Answered

The random variable X follows a normal distribution ?(20,102).
Find P(10<?<35),

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Answered 2021-01-16 Author has 99 answers
Step 1
Normal probability is a type of continuous probability distribution that can take random values on the whole real line. The main properties of the normal distribution are:
-It is continuous (and as a consequence, the probability of getting any single, specific outcome is zero)
-It has a "bell shaped" distribution (and that is where the "Bell-Curve" name comes along)
-The normal distribution is determined by two parameters: the population mean and population standard deviation
-It is symmetric with respect to its mean.
Given : The random variable X follows a normal distribution .
Notation: XN(μ=20,σ2=102)
Step 2
We need to compute Pr(10X35).
The corresponding z-values needed to be computed are:
Therefore, we get:
Not exactly what you’re looking for?
Ask My Question
Jeffrey Jordon
Answered 2021-11-14 Author has 2313 answers

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-02-21

We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 192 had kids. Based on this, plot a 99% confidence interval for the proportion of adult residents who are parents in a given county.
Express your answer in the form of three inequalities. Give your answers in decimal fractions up to three places <p< Express the same answer using a point estimate and a margin of error. Give your answers as decimals, to three places.

asked 2021-03-18

A population of values has a normal distribution with μ=133.5 and σ=5.2. You intend to draw a random sample of size n=230.
Find the probability that a single randomly selected value is between 133.6 and 134.1.
Write your answers as numbers accurate to 4 decimal places.

asked 2022-01-16
You have studied the number of people waiting in line at your bank on Friday afternoon at 3 pm for many years, and have created a probability distribution for 0, 1, 2, 3, or 4 people in line. The probabilities are 0.1, 0.3, 0.4, 0.1, and 0.1, respectively. What is the probability that at most 3 people are in line at 3 pm on Friday afternoon?
asked 2022-01-17
Given 90, 87, 81, 100, 74, 80 what is the mean of the scores?
asked 2022-04-09
Identify an appropriate statistical test and the tail of the test for the following problems. Assume all samples used for the study come from a normal population.
A. Determine if the performance of ABCS 206 students in an interim assessment(IA) is a good predictor of their performance at the end of semester examination.
B. A hair cream manufacturer wants to know if there is a relationship between the quantity of hair cream applied to the hair and the growth of hair.
C. A district health officer wishes to determine if the six villages in his district are independent of residents contracting malaria, schistosomiasis, cholera or tuberculosis.
D. A biologist is studying three different varieties of tomato to determine whether there is a difference in the proportion of seeds that germinate. Random samples of 200 seeds of each of three varieties are subjected to the same starting conditions.
asked 2022-04-24
Given the set: {32,12,54,x,92}, for what x would the mean of the set be -1?
asked 2022-04-16
Last school year student body local university consisted of 35% freshmen 24% sophomores 26% juniors and 15% seniors. A sample of 300 Students taken from this year’s student body showed the following number of students in each classification. Freshmen 90 Sophomores 60 Juniors 90 Seniors 60 What is the expected frequency of seniors?
A- 65
B- 45
C - 35
D- 55

New questions

Linear multivariate recurrences with constant coefficients
In the theory of univariate linear recurrences with constant coefficients, there is a general method of solving initial value problems based on characteristic polynomials. I would like to ask, if any similar method is known for multivariate linear recurrences with constant coefficients. E.g., if there is a general method for solving recurrences like this:
f ( n + 1 , m + 1 ) = 2 f ( n + 1 , m ) + 3 f ( n , m ) f ( n 1 , m ) , f ( n , 0 ) = 1 , f ( 0 , m ) = m + 2.
Moreover, is their any method for solving recurrences in several variables, when the recurrence goes only by one of the variables? E.g., recurrences like this:
f ( n + 1 , m ) = f ( n , 2 m ) + f ( n 1 , 0 ) , f ( 0 , m ) = m .
This second question is equivalent to the question, if there is a method of solving infinite systems of linear univariate recurrences with constant coefficients. That is, using these optics, the second recurrence becomes f m ( n + 1 ) = f 2 m ( n ) + f 0 ( n 1 ) , f m ( 0 ) = m , m = 0 , 1 , .
I am not interested in a solution of any specific recurrence, but in solving such recurrences in general, or at least in finding out some of the properties of possible solutions. For instance, for univariate linear recurrences, each solution has a form c 1 p 1 ( n ) z 1 n + + c k p k ( n ) z k n ,, where c i 's are constants, p i 's are polynomials and z i 's are complex numbers. Does any similar property hold for some class of recurrences similar to what I have written?
I have been googling a lot, but have found only methods for some very special cases (in monographs on partial difference equations, etc.), but nothing general enough. I am not asking for a detailed explanation of any method, but references to the literature would be helpful. I don't know much about transforms (like discrete Fourier transform or z-transform), but I found certain hints that there could be a method based on these techniques. Is it possible to develop something general enough using transform, i.e., is the study of transforms worth an effort (in the context of solving these types of recurrences)? However, it seems to me that the generalization of the characteristic polynomial method (perhaps, some operator-theoretic approach) could lead to more general results. Has there been any research on this topic?