Founded 1991 by Md. Alimullah Miyan
College of Arts and Science
Department of Quantitative Sciences
Assignment of Spring Semester 2024
Instructor Name: Kazi Sabbir Ahmad Nahin
Course Code: STA_240
Course Title: Statistics
Submission Date: 15/04/2024
Full Marks: 100
(Write the answers by hand and the upload a pdf of scanned documents of your hand writing in Google Classroom as well as submit the hard copy in the class. Without the submission in Google Classroom, hard copy will not be accepted. Write your name, ID, and serial no. on the answer script)
1. Roll a balanced die twice. Let,
\( \mathrm{M}= \) the spots resulting the first roll
\( \mathrm{N}= \) the spots resulting the second roll
\( \mathrm{W}= \) the sum of spots resulting \( =\mathrm{M}+\mathrm{N} \)
(a) Find the Probability Mass Functions (PMFs) of M, N, and W.
(b) Draw the Probability Mass Functions (PMFs) of M, N, and W.
(c) Find the expected values of M, N, and W. [Hints: You can use, \( E(W)=E(M)+E(N) \) ]
2. The scores of a reference population on the Wechsler Intelligence Scale for Children (WISC) are normally distributed with \( \mu=100 \) and \( \sigma=15 \).
(a) What percent of this population have WISC scores above 115 ?
(b) What percent of this population have WISC scores between 70 and 130 ?
(c) What score will place a child in the top \( 25 \% \) of the population?
(d) What is the median \( / 2^{\text {nd }} \) Quartile of the score distribution? [Hints: Median \( \left(\mathrm{Q}_{2}\right) \) means \( 50 \% \) of the population]
(e) What is the \( \mathrm{IQR} \) of the score distribution? [Hints: \( \mathrm{IQR}=\mathrm{Q}_{3}-\mathrm{Q}_{1} \), where \( \mathrm{Q}_{3} \) and \( \mathrm{Q}_{1} \) denotes \( 75 \% \) and \( 25 \% \) of the population respectively]
3. There are 7 students in a class: Angela, Jane, Knox, Danny, Johnny, Carter, and Rae. If a Simple Random Sample (SRS) of size 4 is used, how likely Knox is selected?
4. A survey of high school students finds that \( 20 \% \) like Science, \( 15 \% \) like Math, and \( 10 \% \) like both Science and Math. Given a student likes Math, what is probability he/she also likes Science?
5. Chennai Supper Kings, a team in the IPL, plays \( 30 \% \) of their games at night and \( 70 \% \) during the day. The team wins \( 50 \% \) of their night games and \( 60 \% \) of their day games. According to today's newspaper, they won yesterday. What is the probability the game was played at day?