Determine if the following are true or false.a)A random variable is continuous. For any value a, P(X=a)~0 always.b)A standard normal curve means that the mean is 1 and standard deviation is 0.c)For the following probability density function, P(X<2)=2f(x)/1个4The amount of buses that pass through a bus line in 20 minutes is ad)discrete random variable.Focus

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Answered: a) A random variable is continuous. For…

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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The length of eels (in cm) in a river may be assumed to be normally distributed with a mean of μ=46 and a standard deviation of σ=8. An angler catches an eel from a river. Let: X= the length (in cm) of an eel a) If the normal length of eels is between 30 cm and 58 cm, what percentage of eels fall within this normal range? b) What is the probability that an eel is at least 38 cm in length? c) The middle 50% of the lengths (in cm) of the eels are between _ and _
Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ= 1.1 kg and a standard deviation of σ = 4.4 kg. Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is (Round to four decimal places as needed.)
A manufacturer receives a certain component from a supplier in shipments of 100 units. Two units in each shipment are selected at random and tested. If either one of the units is defective the shipment is rejected. Suppose a shipment has 5 defective units. a. Construct the probability mass function for the number of defective units, X, in such a sample and show that it is a valid pmf. b. 2 reasons why is the function is a valid pmf c. Compute the mean and standard deviation of X.
Assume the random variable x is normally distributed with mean u = 88 and standard deviation o = 4. Find the indicated probability. P(77
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The table below represents the probability density function for the random variable X. Find the standard deviation of X Round the final answer to two decimal places. 1/5 2/5 2/5 4 8 O Help copy to ClipboardDownload cSV
Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin. Assuming that a head is six times as kely to occur find the probability distribution of the random variable w Complete the following probability distribution of W w 1. f(w) (Type integers or simplified tractions)
(b) The continuous random variable Z follows a standard normal distribution. Using table, find: PZ>1.11) P (Z 2.46) i. 11. 1ii. iv. V.
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Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal with a mean u= 7500 and a = 1750. A test result of x < 3500 is an indication of leucopenia. This indicates bone marrow depression that may result in a viral infection. a. What is the probability that on a single test x is less than 3500? b. A patient is given 3 tests at regular intervals. What is the probability that the average of the three tests is less than 3500?
Assume the random variable x is normally distributed with mean u= 81 and standard deviation o = 4. Find the indicated probability. P(x< 79) P(x< 79) =(Round to four decimal places as needed.) Enter your answer in the answer box
Let x denote the time taken to run a road race. Suppose x is approx. normally distributed with a mean of 180 minutes and standard deviation of 20 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race a) in less than 156 minutes? b) in 208 to 229 minutes

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