Statistics and Probability Answers

The mathematics club of RAD Senior High School organized a raffle where the prize is the latest edition of a certain brand of the calculator. the raffle aims to raise funds for their club. they were able to sell 1000 tickets that cost 5 pesos each. if they spent 3500 on the prize, what will be the expected gain of a student who will buy one ticket?

find the mean of the probability distribution of the random variable x, which can take only the values 1,2 and 3 given that p(1)=10/33,p(2)= 1/3, and p(3)= 12/33

Dhaka University took a test and the final grades have a mean of 100 and a standard deviation of 11. If we can approximate the distribution of these grades by a normal distribution, what percent of the students

a) scored higher than 120?

b) should pass the test (grades≥90)?

c) should fail the test (grades<90)?

In a deck of cards which consists of cards number 1 to 5 a card is drawn randomly. Each player wins 35 pesos if the number on the card is odd and losses 35 pesos if tge number on the card is even. What is the expected value of his winning?

. A lottery ticket pays off 300,000,000 pesos is made available for 10,000,000 tickets. Each ticket costs 50 pesos. Supposed the variable X gives the net winnings from playing the lottery. What is the expected gain for joining the lottery with only one ticket?

Solve the given problem. Find the following and show your complete solution.

a. Critical Value

b. Margin of Error

c. Confidence Interval

GIVEN:

The average test scores in a Science class is normally distributed with a standard deviation of 8. 200 scores with a sample mean of 170 were selected at random. Estimate the population mean with:

a. 85% confidence

b. 90% confidence

c. 95% confidence

Solve the given problem. Find the following and show your complete solution.

a. Degrees of Freedom

b. Critical Value

c. Confidence Interval

GIVEN:

A sample of six college basketball player had an average weight of 217 pounds with a sample standard deviation of 10 pounds. Find the 95% confidence interval of the true mean weight of all basketball player.

A G's production of 950 manufactured parts contains 70 parts that do not meet the customer requirements. Two parts are selected randomly without replacement from the batch. What is the probability that the second part is defective given that the first part is defective?

Three different machines A1, A2, A3 were used for producing a large batch of similar manufactured items. Suppose that 10% of items are produced by machine A1, 20% by A2, and 40 % by A3. Suppose further that 1% of the items produced by A1, 2% by A2, and 3% by A3 machine are defective. Suppose one item is selected from the entire batch and it is found to be defective. Calculate the probability that this item was produced by machine A2.

QUESTION 1 [25 MARKS] The age distribution of guards hired by the Jumbo Department within the last year is: Age Number 20-29 2 30-39 13 40-49 20 50-59 12 60-69 3 a) Determine the class boundaries of the distribution. (3 marks) b) Construct a histogram and polygon of these data. (3 +3 marks) c) Construct a ‘less-than’ and ‘more-than’ cumulative frequency distribution. (2 +2 marks) d) Draw the ogives. (3 +3 marks) e) Based on the graph, the age of about half the guards hired was less than ….. (3 marks) f) Based on the graph, the age of about 30 of the guards hired was more than ….. (3 marks]