Statistics and Probability Answers

Consider the random experiment of rolling a fair die.
a.) Let X be the number of tosses needed before obtaining a 6. Find the mass function and expected value of X.
b.) Let X be the number of tosses needed before obtaining 3 sixes. Find the mass function and expected value of X.
c.) Let X be the number of sixes obtained in 5 rolls of the die. Find the mass function and expected value of X.

Three people are selected at random. Find the probability:

a. All three share the same birthday.
b. None of the three shares the same birthday.

a box contains 5white and 7 black balls. two successive drawn of 3 balls are made.
1)with replacement
2)without replacement
the probability that the 1st draw would produce white balls and 2nd draw would produce black balls are

1) Suppose 40% of the students in a certain college are female. Suppose further that 15% of the females and 10% of the males are smokers. (a) What fraction of the smokers are female? (b) What is the probability that a student chosen at random is a non-smoker?


2) The time (in hours) a customer spends in a particular store is an exponential random variable T, with E[T] = ½
The time spent in the store by one customer is independent of the 2 number of other customers and their time spent in the store. (a) What is the probability that a customer will spend more than 1 hour in the store? (b) If 5 customers enter the store at the same time, what is the probability that the number of them that remain in the store 1 hour later is 2 or more?

Cardinals Bakery in St. Louis sells baseball player cookes with player names and numbers on them. You are asked to perform study to determine whether baker should produce more with particular players names. Info is as follows: Wainwright, 42, Wacha, 56, Kelly, 38, Martinez 30, Rosenthal 34, Total 200. State the null and alternative hypothesis. Calculate chi square score. Find degree of freedom value. What is the .05 chi-square critical value? What is the .01 chi-square critical value? At a equals .05 is the null hypothesis rejected? What about at .01?

show all the ways in which 3 games of football can be concluded(it can be a win W,a loss L,or a draw X)

two cards are drawn from a pack of deck cards and thrown, after this two more cards drawn together, what is th posibility that both cards have same value?

IV. Solve the problem.
In a certain college in Metro Manila, a study was conducted to determine whether or not the IQ scores of students who came from provincial high schools differ significantly from those students who came from city high schools. An IQ test was given to 200 (100 from each group) college freshmen and the results are as follows:
Students from Prov. H.S.: x1 = 99 and s1= 5
Students from City H.S.: x2 = 102 and s2 = 8
Set up and test the appropriate statistical hypotheses using 0.05 level of significance.

1. Ho:
Ha:

2. α = _______ , _____-tailed test

3. Statistical Test: ____-test, _____-sample mean

4. Area of Rejection:

Tabular Value: _______



Decision Rule:



5. Computation
Formula:




Solution:








6. Decision:

Conclusion:

In the recent board examination for nurses, it is claimed that the average performance of the nurses is 80 with a standard deviation of 5. Would you agree to this claim if a random sample of 100 nurses who took the exam showed an average of 85? Use 1% level of significance.

Let two dice be thrown. What is the probability that the sum on the dice is greater than
or equal to 9?