Statistics and Probability Answers

The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean λ=7.

​(a) Compute the probability that more than 9 customers will arrive in a 2​-hour period.

​(b) What is the mean number of arrivals during a 2​-hour ​period?

Q.No. 1

During 1993, the major earthquakes had Richter magnitudes as shown below.

7.0, 6.2, 7.7, 8.0, 6.4, 6.2, 7.2, 5.4, 6.4, 6.5, 7.2, 5.4

(a) Find mean, median and mode of the above data, and comment it.

(b) Determine interquartile range.

(c) Construct boxplot for outliers.

Q.No. 2

The reaction time to a stimulus for a certain test has a mean of 2.5 seconds and a standard deviation of 0.3 second.

Find the z-score for each reaction time and comment on outlier.

(a) 2.7  (b) 3.9  (c) 2.8  (d) 3.1

Problem. A certain bank issues its own credit card. The head of credit collection  department found out that the mean amount of unpaid balance of the credit card holders was Php 25,000.00 and with a standard deviation of  Php 1,500.00. The head of the bank wanted to find out whether the mean amount of unpaid balance was really Php 25,000.00. He sample 40 credit card holders and found out a sample mean of Php 23,900.00. Can the head of the credit collection department conclude that the unpaid balance is less than Php 25,000.00? Use the 0.01 alpha level. Illustrate the data using a Normal Distribution Curve. Refer the critical value from the Z-Scores Distribution Table or Standard Normal Probabilities Table. 

Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a score between 600 and 700? Calculate the probability.

1. After teaching multiple sections of a statistics course for many years, a professor decides to add an online quiz component to help students review throughout the semester for their final exam. The professor specifically wants to know if adding the online quiz component improves student exam scores. This semester the professor teaches 2 sections of the class with a total of 38 students. The average final exam score for this semester's students is 82.

Over the past many years the professor has taught the course, the average exam score is 75; (σx = 13.5)

The best measure of tendency for the data 2,4,6,810,98,100 is its mean

If you play a game that you can only either win or lose. The probability that you win any game is 35%. If you play the game 45 times, what is the probability that you win 15 if the 45 games, less than 15 games, between 5 and 9 games out of 45?

On average 3 accidents happens every week in a certain city. What is the probability that we will observe 9 accidents in a month

The marks of 500 candidates in an examination are normally distributed with a mean of 45 marks and a standard deviation of 20 marks. Given that the pass marks is 41, estimate the of candidates, who passed the examination