Statistics and Probability Answers

Your math teacher just received 5 new posters for the classroom. In how many ways can she set is up against the back wall?

A study in Batu Pahat General Hospital's on patient account division has compiled data on the age of accounts receivables. The data collected indicates that the age of the accounts follows a normal distribution with mean 28 days and standard deviation 8 days. Ahmad would like to know the probability of the accounts between 20 and 40 days old and the probability of the accounts which less than 30 days old. Shows the calculation of both problems.

Find the regression lines (both) from the following data:
X: 1 2 3 4 5 6
Y: 3 5 6 8 9 11
Also find y for x = 2.5 and x for y=7

The following data is given for X and Y.
X : 2 3 5 7 10 12
Y: 5 9 12 14 15 20 calculate Karl Pearson’s coefficient of correlation
between X &Y

The mean and standard deviation for the life time of a population of light bulbs are
1200 and 50 hours respectively. Assuming these lifetimes are normally distributed,
what is the probability that a light bulb will last over 1500 hours?

Explain the relationship between the Frequency distribution table and the discrete random variable and how to use the Frequency distribution table to find the probability density function, and then explain how to calculate the Expectation, the standard deviation, and Coefficient of variation for it, using students’ bicycles in statistics as a practical example

Given the following data
X 1 3 4 6 8 9 11 14
y 1 2 4 4 5 7 8 9
Determine the least square line using x as independent variable.
Find the estimated value for given values of x and show that
(a) ∑▒Y=∑▒Y ̂ (b) ∑▒〖e_i=o〗

Melina recorded the number of passengers in each car of the first 100 cars that passed in front of her house on Sunday morning. The outcomes are shown in the table below:

Number of Passengers (x_i) 1 2 3 4 5
Number of Cars (f_i) 44 30 15 4 7


Find the mode(M_0) and median(x ̃) value?
Find the mean value(x ̅)?
Find the standard deviation (σ)? (Give your answer in two decimal places).
What is the probability a car to contain:
exactly 3 passengers?
at least 2 passengers?
at most 4 passengers?
exactly 6 passengers?
What kind of probability is the above problem? Justify your answer.

a coin is tossed 4 times what is probability of obtaining 3 heads if it is known that a head has been obtained as the first toss