Description

Assistant: Gizem Su¨ngu¨ Student Id:
Course Policy: Read all the instructions below carefully before you start working on the assignment, and before you make a submission.
• It is not a group homework. Do not share your answers to anyone in any circumstance. Any cheating means at least -100 for both sides.
• Do not take any information from Internet.
• No late homework will be accepted.
• For any questions about the homework, send an email to gizemsungu@gtu.edu.tr.
• Submit your homework (both your latex and pdf files in a zip file) into the course page of Moodle.
• Save your latex, pdf and zip files as ”Name Surname StudentId”.{tex, pdf, zip}.
• The answer which has only calculations without any formula and any explanation will get zero.
Problem 1: (15+20=35 points)
Kuru Kahveci Mehmet Efendi (the producer), which is a coffee brand, supplies coffee beans to a coffee shop (the consumer) in Kadikoy. The coffee is supplied as 50 packages at each order and each package has 1 kg coffee beans. The consumer regards an order as acceptable provided that there are not more than 5 packages which have stale coffee beans. Rather than test all packages in the order, 10 packages are selected at random and tested.
(a) Find the probability that out of a sample of 10, d = 0, 1, 2, 3, 4, 5 are stale when there are actually 5 stale packages in the order.
(Solution)
(b) Suppose that the consumer will accept the order provided that not more than m stale packages are found in the sample of 10.
• Find the probability that the order is accepted when there are 5 stale packages in the order.
(Solution)
• Find the probability that the order is rejected when there are 3 stale packages in the order. (Solution)
1
– Homework #3 2
Problem 2: (20+5=25 points)
(a) Compute the probability that more than 12 customers will arrive in a 3-hour period.
(Solution)
(b) What is the mean number of arrivals during a 3-hour period?
(Solution)
Problem 3: (8+8+8+8+8=40 points)
Given a normal distribution with µ = 35 and σ = 7, find (a) the normal curve area to the right of x = 21.
(Solution)
(b) the normal curve area to the left of x = 25.
(Solution)
(c) the normal curve area between x = 32 and x = 41.
(Solution)
(d) the value of x that has 60% of the normal curve area to the left.
(Solution)
(e) the two values of x that contain the middle 75% of the normal curve area.
(Solution)