Assignment:
1. Consider the following data on distances traveled by 100 people to visit the local park.
|
distance
|
freq
|
|
1-8
|
30
|
|
9-16
|
20
|
|
17-24
|
25
|
|
25-32
|
10
|
|
33-40
|
15
|
Expand and construct the table adding columns for relative frequency and cumulative relative frequency. Then plot Histogram, Frequency Polygon and Ogive Curve.
2. Math test anxiety can be found throughout the general population. A study of 250 seniors at a local high school was conducted. The following table was produced from the data. Complete the missing parts.
|
Score Range
|
Frequency
|
Relative Frequency
|
Cumulative Relative Frequency
|
|
Very anxious
|
|
0.24
|
|
|
Anxious
|
|
|
0.40
|
|
Mildly anxious
|
|
|
|
|
Generally relaxed
|
35
|
|
|
|
Very relaxed
|
|
0.18
|
|
|
|
|
|
|
3. The following frequency table summarizes the distances in miles of 100 patients from a regional hospital.
Distance Frequency
0-4 20
4-8 25
8-12 30
12-16 20
16-24 5
Calculate the sample variance and standard deviation for this data (since it is a case of grouped data- use group or class midpoints in the formula in place of X values, and first calculate the sample mean).
4. At a college, 50 percent of the students are female, and 30 percent of the students receive a grade of C. About 40 percent of the students are male and "not C" students. Use this contingency table.
|
Gender/Grade
|
C
|
Not C or
|
|
|
Female (F)
|
|
|
0.50
|
|
Male (M)
|
|
0.40
|
|
|
|
0.30
|
|
|
If a randomly selected student is a C student, what is the probability the student is female?
5. A and B are independent events. Moreover, P(A) = 0.7 and P(B) = 0.3. Determine P(A B), that is, P(A or B)
6. In a recent survey of homes in a major Midwestern city, 30% of the homes have a fax machine and 75% have a personal computer. Suppose 15% of the homes have both a fax machine and a personal computer. What is the probability that a randomly selected home does not have a fax machine or does not have a personal computer?
7. The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 15%. If 16 calculators are selected at random, what is the probability that more than 5 of the calculators will be defective?
8. An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.40 that troubles in a residential service can be repaired on the same day. For the first 7 troubles reported on a given day, what is the probability that more than4 troubles will be repaired on the same day?
9. Given the length an athlete throws a hammer is a normal random variable with mean 60 feet and variance 9, what is the probability he throws it between 55 feet and 65 feet?
10. If x is a binomial random variable where n = 100 and p = 0.20, find the probability that x is more than 18 using the normal approximation to the binomial. Check the condition for continuity correction.