Statistics Assignment - Statistics 1, Exam 2, Version A

This document presents a complete solution to a statistics assignment, focusing on key statistical concepts. The solution addresses several problems, including identifying discrete and continuous variables, calculating the mean and standard deviation of a probability distribution, applying the binomial distribution to solve probability problems, and working with the normal distribution using z-scores. The assignment covers a range of topics, from basic probability concepts to more advanced statistical analysis, providing step-by-step solutions and explanations. It includes calculations for probabilities, means, standard deviations, and z-scores, and also includes sketches to visualize the problems. The solution also covers the interpretation of statistical results and the application of statistical methods to real-world scenarios.

Running head: STATISTICS 1
Statistics
<Name>
<University Name>

STATISTICS 2
Statistics
1.
(a) The amount of air pressure in a tire of a randomly selected car is a continuous variable
because it is obtained through measurements and can be written even in decimal places.
(b) The number of people who pass through JFK airport terminal in one year is a discrete
variable because it is obtained through counting and we cannot have a half human being.
2. (5 points) Identify the set of all possible values of the discrete random variable, X = the
number of interceptions thrown by a NFL quarterback in one game.
4, 5, 8, 11, 15, and 20
3.
Mean= summation of XP(x)
Which is (0*0.04)+(2*0.27)+(3.3*0.17)+(4*0.12)+(5.75*0.4)
=3.881
Standard deviation is given as
Sqrt of summation(x-mean)^2P(x)
Which is calculated as
Sqrt of (0-3.881)^2*0.04)+(2-3.881)^2*0.27)+(3.3-3.881)^2*0.17)+(4
3.881)^2*0.12)+(5.75-3.881)2*0.4)
=sqrt of 3.112075
Standard deviation=1.76
4.
(a) Construct a probability distribution for X = the number of people in the sample who
passed the bar exam.
P (X=x)=nCx.px.q(n-x), take q=1-p
(b) Find the probability that at least two people in a sample of six passed the bar.
Probaility= nCx.px.q(n-x)
=6C2*0.7^2*0.3^4
=0.06
(c) Find the mean and standard deviation of the distribution.
P=70/100=0.7
Q=1-p
=1-0.7
=0.3
Mean= np
=6*0.7
=4.2
Standard Deviation= SQRTnpq
=sqrt of 6*0.7*0.3
=1.12

STATISTICS 3
5. (10 points)
(a) Exactly 2 of the people say they never make their beds?
Probaility= nCx.px.q(n-x)
=20C2*0.1^2*0.9^18
=0.2852
(b) At least 3 of the people say they never make their beds?
Probaility= nCx.px.q(n-x)
=20C3*0.1^3*0.9^17
=0.1901
6. (8 points)
(a) P(z ≥ 2.86)
From the table, probability is .98169
(b) P(−0.32 ≤ z ≤ 1.45)
From the table, probability is .37448 and .92647
7. (8 points)
Z= m-u/sd
7.02-7.5/1.15
=-0.4174
The proportion, p from z table is .33724

STATISTICS 4
Therefore, probability mean is 33.72%
Sketch
8. (10 points)
Z= m-u/sd
35-5/7
=4.29
The proportion, p from z table is >0.05
Therefore, probability mean is > 99%
Sketch
9.
Z=m-u/sd
0.8=980-u/190
u=186048

STATISTICS 5
10.
Sample mean= mean of population
=45
Standard deviation= var/sqrt n
=8.62^2/sqrt 50
=10.51

STATISTICS 6
11.
Z= m-u/sd
202-192/45
=0.2222
The proportion, p from z table is .58706
Therefore, probability mean is 58.70%
Z= m-u/sd
202-212/45
=-0.2222
The proportion, p from z table is .41294
Therefore, probability mean is 41.29%
Sketch

STATISTICS 7
References
Cho, K., & Jacobs, B. (2017). The EfProb library for probabilistic calculations.