MA ST 2113Homework 4 Instructions: This is assignment is pretty straightforward For

MA ST 2113Homework 4
Instructions:
This is assignment is pretty straightforward
For this assignment, answer questions below (reference notes attached)
Must show all work
Due by July 30th @ 12pm Central/Standard time
Thanks! 😊Top of FormBottom of Form
1 (8 pts). A survey asks people how many TV sets they own in their households. The following table shows the frequency and relative frequency table.
Number of TV sets
Number of households
Relative frequency
1
17
0.16
2
28
0.26
3
36
0.33
4
19
0.17
5
7
0.06
6
2
0.02
Total
109
1.00
Find the average number of TV sets in a household.
2 (8 pts). The grading scale in a class is as follows:
Class participation 4%
Homework assignments 16%
Lab Assignments 7%
Quizzes 8%
Projects 19%
Exams 46%
A student has the following grades:
Class participation 85
Homework assignments 75
Lab Assignments 89
Quizzes 72
Projects 78
Exams 76
Find the student’s overall grade (average grade).
3 (6 pts). The following table is the height probability distribution of a population of 20-29 years old.
Height (X)
Percent
less than 5’7”
15%
5’7”-5’8”
21%
5’9”-5’10”
26%
5’11-6′
19%
6’1”-6’2”
14%
Above 6’2”
5%
Total
100%
Let X denote the height.
Find P(X ≤ 5’10’’).
Find P(X > 6’).
Find P(5’7’’ ≤ X ≤ 6’2’’).
4 (6 pts). Suppose the following is the household income (in dollars per year) in a region.
Let X denote the household income.
Find P(X ≤ 60,000).
Find P(X > 80,000).
Find P(60,000 < X ≤ 100,000). 5 (2 pts). Find the area marked by the dot line: 1.15 1.15 z z 6 (3 pts). Find the area marked by the dot line: -1.9 -1.9 z z 7 (4 pts). Find the area marked by the dot line: -0.56 -0.56 -2.64 -2.64 z z 8 (2 pts). Find P(z ≤ -2.17) 9 (3 pts). Find P(z ≥ 2.9) 10 (4 pts). Find P(-1.6 ≤ z ≤ 0.56) 11 (4 pts). Find the probability values in the boxes of the following graph: 1.49 1.49 z z 12 (3 pts). Find the z-score having an area of 0.1510 to its left. 0.1510 0.1510 z = ? z = ? z z 13 (3 pts). Find the z-score having an area of 0.0821 to its right. 0.0821 0.0821 z z 14 (7 pts). For a normal distribution with mean µ = 6 and standard deviation σ = 3, find P(x ≤ 2.3). x x 2.3 2.3 15 (7 pts). For a normal distribution with mean µ = -1.5 and standard deviation σ = 0.9, find P(x ≥ 0.11). 0.11 0.11 x x 16 (10 pts). For a normal distribution with mean µ = 0 and standard deviation σ = 1.6, find the probability P(-1.54 ≤ x ≤ 1.67). 17 (10 pts). Consider the normal distribution with µ = 11 and σ = 4. Fill in the values in the boxes in the following graph: 14.6 14.6 z z x x z = z = 18 (10 pts). The regular gas price in a city is normally distributed with average (mean) price $3.45 and standard deviation $0.14. (a) Find the percentage of gas stations with gas price less than $3.28. (b) Find the percentage of gas stations with gas price greater than $3.60. (c) Find the percentage of gas stations with gas price between 3.40 and 3.50.