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

University | Universiti Malaya (UM) |

Subject | Statistics |

**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)**

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**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?

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