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MATH 2565 Study Guide - Midterm Guide: Roadside Attraction, Jungle Island, Impulse PurchaseExam


Department
Mathematics and Statistics
Course Code
MATH 2565
Professor
Cindy Fu Yuejiao
Study Guide
Midterm

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York University
MATH 2565 (Winter 2016): Introduction to Applied Statistics
Midterm II Examination – Thursday March 17, 2016, 10 am - 11:10 am
Last Name: Given Names:
Student Number:
Signature :
DO NOT WRITE IN THIS AREA
Read the following instructions carefully
1. Students are allowed to bring: a. One one-sided
8.5”x11” formula sheet b. Calculator(s) (cannot use
laptop, cell phone or ipad as calculator)
2. All work must be done in the free space provided be-
low for each problem or on the back of the preceding
page.
3. No other sheets of paper will be accepted or marked.
4. This exam consists of 9 pages in total. Last 3 pages
contain three tables.
Question Max Score Your Score
1 10
2 10
3 10
4 10
5 10
TOTAL 50
1

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Question 1 (10 marks) Research concerning purchasing habits at the grocery store suggests
that impulse buys make up 60% of all purchases. Suppose 100 customers are selected at
random.
(a) Let Xbe the number of customers who make an impulse purchase out of the 100
randomly selected customers. Find the mean and variance of X.
Solution µ=np = 100(.6) = 60, σ2=np(1 p) = 100(.4)(.6) = 24
(b) Find the variance of the sample proportion ˆp=X
n.
Solution varˆp=p(1p)
n=.6(.4)
100 =.0024
(c) find the probability that at most one customer makes an impulse purchase.
Solution100
0(.4)100 + +100
1(.6)(.4)99 0
2
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