Statistics and Probability Answers

1. If a student randomly guesses at five multiple-choice questions, find the probability that the student gets exactly three correct. Each question has five possible choices.
2. Say 40% of the class is female. What is the probability that 6 of the first 10 students walking in will be female?

5. The probability that a woman does not know swimming is 2/5. If seven women in a city are 

selected at random, find probability that

(i) four women know swimming.

(ii) at least one woman knows swimming

4. A committee of 5 is formed by drawing lots from 8 boys and 6 girls. Find the probability that 

the committee will consist of 2 boys and 3 girls.

The number of traffic accidents per week in a small city has a Poisson distribution with mean 

equal to 1.3. What is the probability of at least two accidents in 2 weeks?

The SSG president claims that the average number of hours the students study their  lesson is more than 25 hours per week with standard deviation of 4 hours. The average of 30  students surveyed is 36 hours per week, is there sufficient evidence to reject the SSG  president’s claim at �� = 0.10 level of significance?  

(a) What is the parameter to be tested?  

(b) Is the population standard deviation given?  

(c) How many samples do we have in this problem?  

(d) What is the given level of significance?  

(e) What is the appropriate statistical test to be used? 

a.leadership skills test a random sample of 200 school managers were administered a developed leadership skills test. the sample mean and the standard deviation were 78 and 4.2 respectively. in the standardization of the test, the mean was 73 and the standard deviation was 8. test for significant difference using a = 0.05 utilizing the p value method. steps (p-value method)

Given a population of 5000 score with mean μ=86 and σ=10. How many scores are below 56?

Activity 1 Find the critical value of the following

Lone-tailed test, or known, a= 0.05; n = 34,

2 two-tailed iest, a unknown, a = 0.01, n=23

3 night-tailed test, a unknown; a = 0.01, n = 15

4 one-tailed test, a known, a = 0.025; n = 37

5 left-tled test, a known, a= 0.05, n = 36

Consider the problem: According to last year's report, a Filipino household spends an average of P500 per day for food. Suppose you recently took random samples of 30 households. You determined how much each households spent for food each day and the results revealed a mean of P450 and the standard deviation of P25.50. Using a 0.05 level of significance, can it be concluded that the average amount spent per day for food of a Filipino household has decreased? Assume normality over the population