Question

Question 1
Suppose that the scores of the semester exam has a normal distribution with mean of 120 and standard deviation of 17. If the bottom 30% of the students failed in the exam.
(1). What was the passing score?

Question 2
A 100-watt light bulb has an average brightness of 1640 lumens, with a standard deviation of 62 lumens. Suppose that the brightness of bulbs follows normal distribution, then

(2). In a lot of 10000 such bulbs, what would be the number of bulbs to have the brightness more than 1800 lumens.
(3). What is the probability that a 100-watt bulb will have the brightness less than 1550 lumens?

Question 3
The piston rings are used to reject when a certain dimension is not within the specifications 2.0±d. It is known that this measurement is normally distributed with mean 1.50 mm and standard deviation 0.20 mm.
(4). Find the value d such that the specifications cover 90% of the measurements.
(5). What is the probability that the measurement of a selected piston ring will be more than 3 mm?

Question 4
Laptops produced by a company last on an average of 5 years. The life span of each laptop follows an exponential distribution.
(6). What is the probability that a laptop will last in less than 3 years?
(7). What is the probability that a laptop will have the life span at least 10 years?
(8). How many laptops from 1000, would be expected to work between 4 and 7 years? (Choose the nearest integer).

Question 5
Let X be uniformly distributed in (2,4) and µ=E(X).
           (9). What is the value of x for which P(X>x+ µ) = 1/4 ?
         (10). What is the value of P( |X- µ| > 2 ) ?

Answer 1

Normal distribution