Statistics and Probability Answers

Software filters rely heavily on “blacklists” (lists of known “phishing” URLs) to detect fraudulent e-mails. But such filters typically catch only 33 percent of phishing URLs. Jason receives 23 phishing e-mails.

The mean time taken by all participants to run a road race was found to 220 minutes with a standard deviation of 20minutes. Using Chebyshev's theorem, find the percentage of the runners who ran this road race in
a) 180 to 260 minutes
b) 160 to 280 minutes
c) 170 to 270 minutes

The table below shows discrete frequency distribution data. Use it to answer the questions that follow.
Class 0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39
Frequency 5 8 10 12 7 6 3 2

Compute;
(i) Mode of the distribution (3marks)
(ii) The 7th decile (3marks)
(iii)The third quartile (4marks)

• solve the question by (i) factorial method, (ii) using venn diagrm:
Q. Four items are taken at random from a box of 12 items and inspected. The box is rejected if more than 1 item is found to be faulty. If there are three items are faulty in the box, find the probability that the box is accepted.

• solve the question by (i) factorial method, (ii) using venn diagrm:
Q. An employer wishes to hire 3 people from a group of 15 applicants, 8 men and 7 women whome are equally qualified, to fill the position. If he selects the three at random, what is the probability that
(i) all three will be men
(ii) at least one will be a woman?

During 2001, 61,3% OF u.S Households purchased ground coffee. These households spent an average of $36.16 on ground coffee during the year ("Annual Product Preference Study". Progressive Grocer, May 1, 2002, 31). Consider the annual ground coffee expenditures for households purchasing ground coffee, assuming that these expenditures are approximately distributed as normal random variable with the mean of $36.16 and a standard deviation of $10.00.
a. find the probability that a household spent less than $25.00
b. find the probability that a household spent more than $50.00
c. What proportion of the household spent between $30.00 and $40.00

2. Potholes requiring repair in a section of a national highway occur at an average rate of 3.2 potholes per kilometer.
a. What is the probability that there are no potholes that require repair in 5 km of the highway
b. What is the probability that at most three potholes require repair in 200m?

A research is conducted to compare two weight loss diets, Diet A and Diet B. 30 subjects follow Diet A and 30 subjects follow Diet B for a year. At the end of the year, the weight loss (in kg) of each subject is recorded. Table 1 shows several descriptive statistics and Figure 1 represents the boxplot of weight loss for Diet A and Diet B. By using Table 1 and Figure 1, answer the following questions: Table 1: Descriptive Statistics for Diet A and Diet B Weight Loss (kg) Data Diet N Minimum Q1 Median 03 Maximum Diet A 30 0.462 3.453 6.415 8.548 13.599 Diet B 30 0.200 2.037 4.157 7.716 15.491
(a) Which diet appears to he more effective? Give reason for your choice.

If p(A)=0.5, p(B) = 0.25, and A and B are independent.

- what is value of p(A&B)?

- what is value of p(A|B)?


Notes:
A & B are independent if P(A) = P(A|B)
When A & B are independent, then P(A&B) = P(A) x P(B)

P(A or B) = P(A) + P(B) - p(A+B)

Q. If a no. is randomly choosen from following list:
32,49,55,56,28,50,40,40,45,3,25.
What is probability that the no. is multiple of 5?

Q. A bag contains 9 red, 2 blue and 3 green marbles. What is the probability of randomly selecting a non-blue marble from bag.