Statistics and Probability Answers

1. It is known that a probability of a male child birth in a family is known to be 0.6. Find
the probability that out of 6 births recorded in the family
a) There will be exactly 3 male children.
b) There will be at least two male children
c) There will be no female child.

Let X~Bin(n,p).Find E(e^tx) where t is a constant

If X has a Poisson distribution with parameter λ, and if
P(X=0)=0.2.
Evaluate
P(X>2).

b. What are the two major classifications of single-factor experiments?
c. Complete the analogy:

Paired Observation: Test of Hypothesis = _____________ : ANOVA

d. Blocking is usually used to reduce the error by eliminating the ____________ factor.
e. To compute for the F-value, we divide the mean square of the treatment or factor by the __________________________.

The following data show the effect of 4 operators, chosen randomly, on the output of a particular machine.
operator 1: 175.4 171.7 173.0 170.5
operator 2: 168.5 162.7 165.0 164.1
operator 3: 170.1 173.4 175.7 170.7
operator 4: 175.2 175.7 180.1 183.7
(a) Perform al analysis of variance at the 0.01 level of significance. (b) Compute an estimate of the operator variance component and the experimental error variance component. What inference(s) can you make based on the computed variance components?

Apply Chi-square test to check whether the data given below may be regarded as conforming to a Poisson distribution.
X 0,1,2,3,4,5,6,7 and
Y 305,363,211,81,28,9,2,1

Select Six Lottery involves picking five different numbers from 1 to 35, plus a sixth bonus number, which may be the same as one of the initial five numbers.
a) First prize of $1 000 000 is paid if a ticket matches the five initial numbers and bonus number. What is the probability of this happening?
b) Second prize of $250 000 is paid if a ticket matches the five initial numbers, but not the bonus number. What is the probability of this happening?
c) Third prize of $100 000 is paid if a ticket matches the bonus number and four of the five initial numbers. What is the probability of this happening?
d) What is each ticket worth, if it costs $5 to play?

Three six-sided dice were thrown 648 times and the number of 5's or 6's noted at each throw. test the hypothesis that the data have a binomial distribution. use α=0.05.
Number of 5's or 6's 0,1,2,3
Number of throws 179,298,141,30

There are three options for the meal choice on a flight on a particular air route: beef, fish and vegetarian. Over many flights it has been observed that the probability that a passenger chooses beef is 0.5917. For a sample of 322 passengers on one flight what Z value would you use to find the probability that more than 55.26% of passengers request beef? Give your result rounded to four decimal places