$MathMaster logo$

MathMaster

Home
general
let x be a continuous random variable that is normally distributed with mean u 15 and standard deviation 2 8 find p 12 2 x

Question

Let X be a continuous random variable that is normally distributed with mean, µ = 15 and standard deviation, σ = 2.8, find P( 12.2 < x < 18.36). Answer should contain 4 decimal places and enter in the form 0.XXXX

179

likes

893 views

Answer to a math question Let X be a continuous random variable that is normally distributed with mean, µ = 15 and standard deviation, σ = 2.8, find P( 12.2 < x < 18.36). Answer should contain 4 decimal places and enter in the form 0.XXXX

$Expert avatar$

4.8

105 Answers

The probability that the continuous random variable \( X \) falls between 12.2 and 18.36, given that \( X \) is normally distributed with a mean (\( \mu \)) of 15 and a standard deviation (\( \sigma \)) of 2.8, is approximately 0.7263 or 72.63%.

Frequently asked questions (FAQs)

Math question: Find the area of a triangle with side lengths 5, 12, and 13 using Heron's formula.

+

Question: What is the absolute maximum and minimum values of the function f(x) = 3x^2 - 4x + 1 in the interval [0, 5]?

+

Math Question: What is the result when you divide 3/5 by 2/3?

+

New questions in Mathematics

The random variable Y is defined as the sum between two different integers selected at random between -4 and 2 (both included). What are the possible values of the random variable Y? What is the value of P(Y=-3)? And whether it is less than or equal to -5?

*Question!!* *Victory saved 3,000 in first bank and 2,000 Naira in union bank PSC with interest rate of X% and Y% per annual respectively his total interest in one year is #640. If she has saved 2,000 naira with first bank and 3,000 naira in union bank for same period she would have made extra 20# as additional interest, then find the value of X and Y

Moaz wanted to test whether the level of headache pain (on a scale of 1 – 10) changes after taking Advil. He collected data from 9 participants and calculated the difference in headache pain before and after taking Advil (summarized in the table below). Determine W observed for this test. Difference Scores -2 -4 0 +1 +3 -2 0 -3 -5 Also, What is the degrees of freedom for this test?

Director of reservations believes that 9% of the ticketed passengers are no-shows. If the directors right what is the probability that the proportion of no-shows in a sample of 789 ticketed passengers with differ from the population proportion buy more than 3% round your answer to four decimal places.

4. Show that if n is any integer, then n^2 3n 5 is an odd integer

Mrs. Emily saved RM10000 in a bank. At the end of the eighth year, the amount of money accumulated amounted to RM19992.71. If the bank pays an annual interest of x% for a year compounded every 6 months. Calculate the value of x.

The Humane Society has asked for our help again this week. Currently they are charging $50 for an adoption fee. Unfortunately they just pulled this number out of the air and do not know why they are charging this amount. They would like to charge an amount that covers all the adoption costs – both the variable costs for adoptions as well as the fixed cost for the kennel portion of the Humane Shelter operations. We can help them by doing a breakeven analysis. During a client meeting we gathered these facts. There are 2 part-time employees that each earn $1000 per month. The utilities for the kennel area (water, electricity) are $200 per month. The average food cost for animals in the kennel is $800 per month. In addition, each animal that is adopted receives a rabies vaccination that costs $4 and is micro-chipped that costs $6. At the current cost of $50, how many animals must be adopted to break-even? What would break-even be at a $60 adoption fee? What would break-even be if the fee were lowered to $40? The newspaper has suggested that the Humane Society advertise to increase pet adoptions. The package that they have recommended costs $1000 for a very small ad run every day for a month. If the Humane Society does this extra advertising, how will it affect breakeven? Based on what you have learned about elasticity, what price do you recommend for the adoption fee?

Your boss asks you to plan the sample size for a randomized, double-blind, controlled trial in the clinical development of a cure for irritable bowl disease. Current standard treatment shall be compared with a new treatment in this trial. The S3-guideline of AWM demonstrated a mean change of the summary score of the validated health related quality of life questionnaire at 8 weeks of 16 with standard deviation 23 under standard treatment. You quote the drop-out rate of 11% from literature (previous phase of clinical development). Your research yielded a clinically important effect of 4 that has been found to be the Minimal Clinically Important Difference (MCID). In order to demonstrate superiority of the new treatment over standard of care, you assume that the change in of the summary score of the validated health related quality of life questionnaire follows a normal distribution, and that the standard deviation is the same for both treatments. How many patientes would one need to recruit for the trial to demonstrate the clinically interesting difference between treatments at significance level 5% with 95% power?

A company receives sales in $20 per book and $18 per calculator. The per unit cost to manufacture each book and calculator are $5 and 4$ respectively. The monthly (30 day) cost must not exceed $27000 per month. If the manufacturing equipment used by the company takes five minutes to produce a book and 15 minutes to produce a calculator, how many books and calculators should the company produce to maximise profit? Please solve graphically and

A machine produces 255 bolts in 24 minutes. At the same rate, how many bolts would be produced in 40 minutes?

A bag has 4 green lollipops, 3 white lollipops, and 1 black lollipop. What is the probability of drawing a white lollipop?

Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.

The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion is greater than 35%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is z= 2.6. Find the P-value for this test.

a survey showed that 3 out of 7 voters would vote in an election. based on this survey, how many people would vote in a city with 25,000 people?

Let x be an integer. Prove that x^2 is even if and only if is divisible by 4.

Which statement best describes the key changes in perspectives on inclusion? An inclusive program must consider the unique experiences of every child and family as well as the child's strengths and needs. There is a shift in thinking about individual programs as "inclusive programs" to thinking about inclusion as something that reflects the cultural influence of the family. There is a greater emphasis on barriers to full participation and the acknowledgement that all children are unique and must be fully and meaningfully engaged in a program. In an inclusive program all participants are accepted by their peers and other members of the community.

find missing measure for triangle area = 48 m square base = 10m heaighy = ? m

1. A jeweler has two gold bars, with 80% purity and the other with 95% purity. How much of each must be melted to obtain a 5 kilo ingot with 86% purity?

A post office has three categories of letters: 60% are from businesses, 30% are individual mail, and the remaining 10% are government mail. 5% of the letters from businesses have address errors, 10% of the individual mail has address errors, while 1% of the government mail has address errors. If we receive a letter with an address error, what is the probability that it is individual mail?"