b)Universiti Teknologi MARA Cawangan Pahang has conducted a survey to know theperception of the students towards online and distance learning. A mail questionnairewas distributed. The proportion of people who respond to a certain mail questionnaire isa continuous random variable X, which has the probability density function as follow;ii)i) Find the expected value of Xiii)f(x)- {1/16 (x + 2)Find V (2x - 2)Calculate the variance of X0

Given,f(x)=116(x+2); 0<X<40; elsewhere

Answered: b) Universiti Teknologi MARA Cawangan…

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...

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Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.2 mg/L with 95% of the data ranging from 5.4 mg/L to 13.0 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume xhas a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L?(Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…
Bliss Biscuit Company manufactures packets of Devine biscuits and has found that the weight of the packets is a continuous random variable which follows a normal distribution with a mean of 297 grams and standard deviation of 1.8 grams. a) What is the probability that the packets will weigh less than 293 grams? b) What percentage of packets will weigh more than 300 grams? c) What is the probability that the packets will weigh less than 293 grams or more than 300 grams? d) 20% of these packets weigh above a particular weight. What is that weight? e) Find the probability that the packets will weigh between 295.5 and 298.5 grams?
The manager of a baseball team has determined the number of walks, x, issued in a game by one of the pitchers. The probability distribution for x is as follows: P(x) 1/20 X 1 2/20 2 3/20 3 11/20 4 3/20 a) Is this a correct probability distribution? Why or why not? b) Calculate the mean (expected value) for x. c) Construct the probability distribution histogram for the number of 'walks'.
It is known that a certain lacrosse goalie will successfully make a save 91.83 percent of the time. Suppose that lacrosse goalie attempts to make 11 saves. A) What is the probability that the lactose goalie makes 8 saves B) Let x be the random variable which denotes the number of saves that are made by the lacrosse goalie. Find the expected value and standard deviation of the random variable. E(X)= O=
The weight of a male bald eagle has approximately a normal distribution with mean ?= 7.4 pounds and a standard deviation of ?= 1.6 pounds. Suppose we take a random sample of n=64 male bald eagles. Let X̄ be the random variable representing the mean weight in pounds of the 64 sampled male bald eagles. Let Xtot be the random variable representing sum of the weights of the 84 sampled bald eagles. a) About what proportion of male bald eagles have weights between 7.0 and 7.8 pounds? b) About what proportion of male bald eagles have weights greater than 7.8 pounds? c) About how many of the 64 sampled male bald eagles would you expect to have weight greater than 7.8 pounds? (nearest integer)? d) About how many of the 64 sampled male bald eagles would you expect to have weight between 7.0 and 7.8 pounds? (nearest integer)? e) What is the standard deviation of the distribution of X̄ (in pounds)? f) What is the standard deviation of the distribution of Xtot (in pounds)? g) What is the…
Q4 For the tornado events in a certain region, the tornado-induced wind speed can be modeled by a lognormal random variable with a mean value of ux = 120 mph and a standard deviation of ox = 12 mph. a) Calculate the probability that the wind speed will be between 100 mph and 130 mph in a tornado event. b) If a structure located in this region is designed to resist for wind speed of 150 mph, what is the probability that the structure will be damaged during such a tornado?
A Engr. Juan dela Cruz is in-charged of ensuring the quality of products and services produced by their beverage company located in Southern Luzon. One of their products is bottled cranberry juice. He observed that the amount of juice drink in each 32 mL bottle is actually a normally distributed random variable, with a mean of 32.2 mL and a standard deviation of 0.3 mL. a) Find the probability that, if a customer buys one bottle will contain less than 32 mL. b) Find the probability that, if a customer buys a cartoon of four bottles, the mean of the four will be less than that of 32 mL.
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A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by

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