EIA1005: Let X be a continuous random variable with the following probability density function: Statistics Assignment, UM, Malaysia

Question 1

Let X be a continuous random variable with the following probability density function

a) Evaluate 𝑐
b) Find 𝐹(𝑥)
c) Use 𝐹(𝑥) to find 𝑃(1 ≤ 𝑋 ≤ 2)

Question 2

The mean daily milk production of a herd of goats has a normal distribution with a mean of 70kg and a standard deviation of 13kg. What is the probability that

a) the milk production for a goat chosen at random will be less than 60kg?
b) the milk production for a goat chosen at random will be greater than 90kg?
c) the milk production for a goat chosen at random will be between 60kg and 90kg?

Question 3

An assessment test is used to measure a person’s readiness for college. The mathematics
scores in the test are scaled to have a normal distribution with a mean of 500 and a standard deviation of 100. What proportion of the people taking the test will score below 350? Remedial assistance will be given to students in the bottom 10%. What is the maximum score of this group of students?

Question 4

A certain type of thread is manufactured with a mean tensile strength of 78.3kg and a standard deviation of 5.6kg. Assuming that the strength of this type of thread is distributed approximately normal, find

a) the probability that the mean strength of a random sample of 10 such threads falls between 77kg and 79kg
b) the value of x to the right of which 15% of the means computed from random samples of size 10 would fall.

Question 5

It is known that a particular machine produces 10% defective electrical components. A box of 100 items of these electrical components will be rejected by a buyer if more than 11% of the items are defective. Buyer A ordered 200 boxes of these electrical components. How many of these boxes will be rejected by buyer A?

Answer

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