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Directions: Read, analyze, and solve the problems below. Show your complete solutions.
a. What is the probability that the 36 tires will have an average of less than 16,000 miles until the tires begin to wear out?
b. What is the probability that the 36 tires will have an average of more than 18,000 miles until the tires begin to wear out?
3 The number of driving miles before a certain kind of tire begins to show wear is on the average, 16, 800 miles with a standard deviation of 3, 300 miles.
2 The average number of pages in a novel is 326 with a standard deviation of 24 pages. If a sample of 50 novels is randomly chosen, what is the probability that the average number of pages in these books is between 319 and 331?
1 There are 250 dogs at a dog show that weigh an average of 12 pounds, with a standard deviation of 8 pounds. If 4 dogs are chosen at random, what is the probability that the average weight is greater than 8 pounds?
In a class 100 students how much minimum number of students is there whose first name begin with the same alphabet
Find P.D. from B.D. using Stirling’s approximation.
The acceleration of a particle at any time is given by a = 12e
3t
i − 8sin2tj +
4tk. If the velocity is zero at t = 0, find velocity.
A machine producing hair pins produces 1 defective out of 400 on an average. If 100 hairpins are packed in each box.
In above problem, suppose the manufacturer gives guarantee that there will be less than 3 defectives in a box of 100. What is the probability that a box selected at random will meet the guarantee.
Translate each of these quantifications into English language and determine its truth
value.
1. ∃x∈R (x3 = −1)
2. ∀x∈Z (x2 ∈ Z)
Given a random variable with binomial distribution use moment generating technique to determine the mean
Trace the curve , x^2= y^2((x+1)^3 ) stating all the properties used in the process.
Use existential and universal quantifiers to express the
statement "Everyone has exactly two biological parents"
using the propositional function P(x, y), which represents
"x is the biological parent of y."
Express this statement using quantifiers: "Every student
in this class has taken some course in every department
in the school of mathematical sciences."
